Tanjiro is considered to be Muzan's main nemesis throughout the series. After murdering the Kamado family, he was personally sought out by Tanjiro in Asakusa, Tokyo when the Demon Slayer recognized his scent from the scene of the murder. Although Muzan had never met Tanjiro before then, he knew immediately that he needed to eliminate him after recognizing the hanafuda earrings he wore to be the ones his would-have-been killer previously donned, as later revealed. In an attempt to flee, he created a diversion by transforming a young man into a Demon to deter Tanjiro, but not before Tanjiro professed his goal to chase Muzan to the ends of the earth in order to kill him. Enraged by his threats, Muzan would send multiple Demons to kill Tanjiro such as Yahaba, Susamaru and Enmu throughout the series.
As mentioned, it is revealed that Muzan's desire to destroy Tanjiro stemmed from his hatred towards his previous nemesis, Yoriichi Tsugikuni. After recognizing the earrings Tanjiro wore in Asakusa, Muzan realized that he was a Sun Breathing user, a wielder of the incredibly powerful technique Yoriichi had developed and that Muzan had sworn to eradicate its users after it almost killed him. This is why, upon seeing Tanjiro for the first time, the Demon Lord felt threatened and became frantic in trying to kill him.
As Muzan begins to disintegrate, he becomes so overwhelmed with emotion that he decides to pass on his dream to Tanjiro. After realizing his abilities to use the Sun Breathing, Muzan decides that Tanjiro is capable of surviving to make his dream come true, and become the King of Demons.
At the very beginning of the story, Muzan tried to turn Nezuko and the entire Kamado Family into Demons, however all of them failed to survive the transformation, except for Nezuko. He soon found her to be a defiant nuisance much like Tamayo, able to escape his curse and become uncontrollable. However after Nezuko developed a resistance to sunlight, Muzan didn't hesitate to attack the Demon Slayer Corps alongside the remaining Upper Ranks Demons in an attempt to devour Nezuko and achieve his long-sought desire to become invincible.
Later on when Nezuko regained all of her memories, including the painful and traumatizing memories of losing her family to Muzan in his attack on her home, she is shown to harbor immense hatred and rage towards the Demon's actions and was shown to barely be able to control herself as it all came back to her. As shown in her recollection, Muzan was shown to have attacked the Kamado family purely out of a whim, with him later injecting Nezuko with a gigantic amount of his blood only to see if she could survive or not, when she had seemingly died, Muzan was shown to have been initially disappointed and wondered if he could ever create a demon that could resist the sun.
Muzan's animosity towards Kagaya can almost be described as professional as opposed to personal. The Ubayashiki family is the core of the Demon Slayer Corps. Kagaya, as it's head for the vast majority of the series, could be described as Muzan's greatest foe by virtue of that position. Even when they meet, Muzan doesn't paticularly display or feel any real animosity, toward Kagaya, though he does seem to think he and his family are a pack of weirdos.
When he first encountered Yoriichi, Muzan was arrogant and stated that he wasn't interested in Demon Slayers who use Breathing Styles, before dismissively attacking Yoriichi as if he'd be an easy kill. However, much to his surprise, Yoriichi struck him multiple times with his bright red blade, wounding him with deep slashes that the Demon Lord was unable to regenerate. Muzan quickly fled the scene, barely still alive, and developed a loathsome fear of the Breath Style Progenitor, prompting him to systematically murder all of the other Sun Breathing users to prevent anyone else like Yoriichi from emerging.
Even 400 years later, Muzan's fear of Yoriichi remained fully intact, as simply laying eyes on Tanjiro's hanafuda earrings caused him to recall their clash. Although Yoriichi was long dead, his visage appeared in the blood memory of Daki after Tanjiro awakened his Demon Slayer Mark, causing Muzan's fear to once again grow.
In their initial encounter, Muzan turned Tamayo into a Demon in order to cure her disease, hiding from her the true consequences of the transformation and so causing the death of her husband and kids. Much like Nezuko, Muzan views her as a nuisance to him after she was freed of his control, and desires for her to be killed. He didn't hesitate to mock Tamayo about killing her husband and children as well as going on a rampage out of despair killing other humans in the process, placing all the blame on her without taking responsibility for any of it.
Prior to this, hundreds of years ago, Tamayo had attempted to kill Muzan. However, upon realizing that she stood absolutely no chance of winning, Tamayo's mental state was completely defeated, her resolve and determination replaced by a docile, servant-like demeanour.
However, upon witnessing Yoriichi's immense power and skill during his fight with Muzan, Tamayo's resolve to kill him was reignited, causing her to once again refocus her efforts onto defeating the Demon Lord and restart her research into creating drugs for weakening or killing him.
Based on the familiarity in which the two conversed at the end of the story, and the fact that she was beside him when he fought Yoriichi, suggest that he did have some fondness for Tamayo, though why in never covered.
The Demon Slayer Corps has been fighting and battling Muzan and his created demons since the beginning of the demon race's spread to the entirety of Japan during the time of Antiquity and as such are Muzan's eternal enemies in a thousand year struggle, where the Corps have attempted time and time again to kill him and end his threat to humanity and his own struggle to annihilate them and put a stop to their constant attempts at his life and ruining and interfering with his plans.
During the Corp's early history before the creation of the Breathing Styles, it was implied by Muzan that he himself never considered them to be any great threat to him or his plans and initially considered them as mere minor annoyances due to the fact that they initially barely posed a genuine threat to him and his demons.
However with the joining of Yoriichi Tsugikuni and his invention and spread of the Breathing Styles Techniques, Muzan gradually became more and more aware of them and keep a much more keen eye on the rapidly growing organization due to the now substantial threat they now posed to him as they began to annihilate his created demon's by the hundreds thanks to their newly acquired techniques.
However despite this and due to his own immense arrogance and inflated ego, Muzan himself initially bared little to no fear for the newly empowered demon slayers and in fact instead became curios with the slayers themselves during the initial years of the Slayer's "Golden Age" and the specific changes and enhancements their breath styles did to their bodies and instead developed the desire to study these physical enhancements up close to help his own research. Eventually to satiate this curiosity, Muzan approached and calmly asked a single Demon Slayer if he wanted to become a demon and convinced him to turn due to observing that due to the immense power that certain demon slayers obtained their bodies were fated to die at age 25, targeting the man's desire to become stronger and live longer and successfully convincing him to defect and join him.
Eventually, upon convincing the renegade Demon Slayer to transform into a Demon, Muzan successfully researched and studied his physiology and biology as a powerful Breath User and the enhancements further done to his body upon transforming into a Demon. After doing so, Muzan stated that he had then lost nearly all interest in the Demon Slayers.
However this mindset quickly changed upon nearly being killed by Yoriichi Tsugikuni. Muzan quickly became more vicious and paranoid with the Demon Slayer Corps upon realizing that people that can genuinely kill him do indeed exist and that the techniques to do so are found only with the Corps, causing the demon progenitor to now take more active attempts to annihilate the Demon Slayer Corps and began taking much more careful and intricate steps to further insure his own safety for the next hundred years due to his heightened paranoia. During of which Muzan and his subordinate insured to eliminate each and every single person both in and outside of the Corps that know the Breathing Style of Yoriichi to further insure that no one can learn them and has begun actively sending his strongest demon's to eliminate the Corp's strongest members to insure no one else of Yoriichi's power can appear ever again.
Muzan himself, due to his selfish mentality and arrogant point of view and inflated ego, has deemed the Demon Slayer Corps as a group of unnatural,obsessive freaks who continuously chase after him for no reason due to his own belief that he and his demons are something akin to a natural disaster, something that is indeed destructive and kills people, but something completely unavoidable and natural. And that the demon slayers are "strange" due to them holding a grudge over losing their loved ones to them and comparing their justified anger to something as ridiculous as holding a grudge and picking a fight with air,fire,earth or water whenever there is a earthquake,flood,forest fire,storms or twisters that kills their family.
The Ubuyashiki Family have been leading the Demon Slayer Corps since the times of antiquety and have continued to do so for a thousand years in their mission to kill the Demon Progenitor. Due to them being the main ringleaders of the Demon Slayer Corps, Muzan deeply despises the Ubuyashiki Family and for centuries, has made it one of his top prioraties to eliminate the entire clan and end their bloodline in order to permenently rid of himself of the Demon Slayer Corps. This is seen where Muzan clearly stated to his Upper Ranks that the Ubuyashiki Family themselves is one of the primary targets they need to eliminate and one of the primary reasons why Muzan was so disappointed and enraged with them was due to their lack of success in permanently ending the Ubuyashiki Family.
As revealed by Kagaya Ubuyashiki, the Ubuyashiki family themselves are in fact related to Muzan by blood, with them being the descendants of his relatives from a thousand years ago. According to Kagaya, the Ubuyashiki bloodline was cursed for having produced the Demon Progenitor and all the children born into their clan was stated to have been sickly and weak, dying before they were even fully grown. After consulting a priest, his relatives were told the reason for their curse was due to Muzan having orginated from their bloodline and they should devote their lives and their clan into killing him and purging the world of his demons in order to remove their curse. From then hence forth, the Ubuyashiki family would receive their spouses selected for them by Priests, and since then, while those born to the clan still died before they became thirty, they were now at the very least, more resistent to death.
However despite this blood relationship to him, Muzan himself expressed no compassion nor emotional attachment to the family and instead has stated to actually feel sickened by them, as seen during his conversation with Kagaya, where he mocked him and his family for their centuries long resolve to kill him.
Muzan holds these Demons in quite a high regard compared to the others, giving them a larger portion of his blood to increase their powers. Despite favoring them more than regular Demons, Muzan tends to show that he prefers the Upper Ranks compared to the Lower Ranks. This is evidenced when Muzan killed off the Demons during the Lower Ranks meeting out of anger following Rui's defeat, and his criticism of their failure to win against the Demon Slayers and their apparent inability to defeat the Hashira's of the Corps and considered them to be arrogant, negligent failures due to them becoming overly confident at the fact that they became Lower Ranks. However despite Muzan's preference to them, he still views the Upper Ranks as inferior due to the verbal abuse towards them for failing to find the Blue Spider Lily after hundreds of years of searching and their apparent failure to completely destroy the Demon Slayer Corps from existence and eliminate the Ubuyashiki family. In the end, he viewed them all as expendable tools and after emerging from his flesh cocoon to face the Demon Slayer Corp, admonished them all for being useless before declaring that he alone will kill the Demon Slayers.
Muzan first met him when he was known as Michikatsu Tsugikuni, the latter had long desired to become as powerful as his brother but failed, as well as fearing his imminent close death by bearing the Demon Slayer Mark. Muzan persuaded him to change, noting they would both win, as he could live forever and become stronger whereas Muzan would gain a Breathing Style using demon. Taking the name Kokushibo, he became Muzan's most powerful subordinate and was Upper Rank One of the Twelve Kizuki.
He was arguably one of the closest to Muzan, who viewed him as somewhat of a business partner.In turn, Kokushibo became intensely loyal to Muzan, acting as an enforcer for the hierarchy he built among the Upper Ranks, as shown when he punished and threatened Akaza for attacking Doma. Kokushibo and Muzan were jointly responsible for nearly eradicating Sun Breathing entirely, after the latter's encounter with the former's brother Yoriichi Tsugikuni.
Muzan is shown to have a positive master-servant relationship with Daki, as the young Demoness seemingly worships and admires the Demon Progenitor immensely, fervently hanging on each and every one one of his words and doing her absolute best to accomplish the tasks he gives her.
Muzan, in turn, aware of Daki's easily trusting and therefore exploitable personality, takes full advantage of her worship by regularly complimenting her, calling her a "special" Demon in order to reinforce her loyalty to him. However, in truth, as revealed after her death, Muzan sees Daki as a tool to keep her brother, Gyutaro, in line, deeming her to be the main reason why the "true" Upper Rank 6 was killed and in truth does not think highly of her and deeming her as someone not very intelligent.
Due to his favoritism to the siblings (particularly to Gyutaro), Muzan was noted to give them the special privilege to actually share the position of Upper Rank 6 between the two of them, something not even seen among any of the other higher ranked Upper Ranks.
In truth, Muzan only ever saw Gyutaro as truly being worthy of being his Upper Rank 6, as revealed when Muzan claims that he highly valued him and expected him to grow more powerful due to his greedy, apathetic and violent personality. However, Muzan also seems to look down on Gyutaro due to him believing that his love for his sister was holding him back and that the main reason he was killed was because of her.
During the first gathering of the Upper Ranks in hundreds of years, Muzan is shown to particularly dislike Gyokko due to his arrogant and somewhat insolent personality clashing with Muzan's own short temper and narcissism, seen when he angrily ripped off Gyokko's head when the Demon attempted to appease his Lord.
Gyokko, however, despite being brutally beheaded by him, showed absolute loyalty to the Demon Progenitor, as seen when he showed no fear, pain or anger at Muzan's actions but was instead overjoyed by Muzan holding his severed head in one hand. showing a fanatical amount of loyalty to him and was slightly annoyed by Muzan blowing him off despite him obtaining vital information on the Demon Slayer Corps but in the end considered this a good point of Muzan's personality.
Later it was revealed that Muzan in fact considers Gyokko to be one of his favorite Upper Ranks due to his pots, with him greatly liking to the artistic skill he puts into them and the high price he gets by selling them.
Hantengu is seen to be incredibly fearful towards Muzan, especially during the Demon Lord's more violent and moody episodes, as seen when he was constantly cowering in fear of him and constantly apologizing to him during the meeting of the Upper Ranks after Gyutaro and Daki's deaths putting him in a bad mood. But nonetheless Muzan is still shown to possess a level of trust in Hantengu's abilities and powers as a Demon despite his cowardly nature, as seen when he trusted him enough to accompany Gyokko in a mission after the meeting was adjured.
Later it was revealed that Hantengu follows Muzan not out of fear of him, but due to him being genuinely loyal and grateful to the Demon Lord. This was due to Muzan having "saved" Hantengu from being executed by a "corrupt" Magister who did not believe Hantegnu's claims of being "innocent" of the crimes of theft and murder by transforming him into a Demon and freeing him from prison before his execution date. Thanks to this Hantengu believes that Muzan was the first person to "truly" see his "innocent self" and "believe" him, causing the Demon to then harbor a deep sense of respect that is even present in his other radically different disposition clones.
Upon his death at the hands of Tanjiro Kamado, Muzan was absolutely delighted by Hantengu, due to him successfully reporting that a Demon that can withstand sunlight has appeared, causing the Demon progenitor to laugh in ecstatic delight and actually compliment the Upper Rank on his work.
Muzan in turn sees Hantengu as an "ordinary person" and sees his overly cowardly/submissive personality as annoying, but tolerable.
Nakime's exact relationship with Muzan is unknown, but she herself has shown to be incredibly loyal and obedient to the Demon Lord out of genuine loyalty instead of fear, as seen where she would stoically follow each and every order given to her by Muzan without hesitation.
After becoming an Upper Rank and replacing Hantengu, Muzan is shown to have become genuinely impressed and appreciative of Nakime's growth in her abilities and the further development of her powers, as seen where he actually complimented her on her growth and even thanked her for successfully completing her mission of locating each and every Demon Slayer across the country and locating Kagaya Ubuyashiki himself, a rarity due to Muzan's own view of only seeing the Upper Ranks as expendable tools and the usual degrading/arrogant/condescending demeanor he usually shows when interacting with them.
She was one of Muzan's favorite Upper Rank, since he believes her ability to be exceptionally useful.However, he showed no qualms about killing her after Yushiro took control of her vision.
Muzan had first met Akaza when he was originally known as Hakuji, having first met the boy after he had revenge for his teacher and fiancée's murders by killing the Kenjutsu Dojo brutally. Muzan having heard of the carnage and the sheer brutality of the mutilated corpses of the victims was under the assumption that a Demon was responsible for the killings, confusing the Demon Lord due to not having sent any into the region of the killing's location causing him to then go to the place in order to investigate out of curiosity.
Having found him shortly after the dojo's destruction, Muzan was both surprised and disappointed to learn that the killer was in fact nothing more than a normal human. After Hakuji threatened to kill him, Muzan rushed forward and pierced his head, before declaring his intentions to form the Twelve Kizuki and asked if he was able to withstand his blood.
Eventually Hakuji, now known as Akaza, had fully reached Muzan's expectations and did indeed become one of his Kizuki, specifically his Upper Rank 3, delighting the Demon Lord and causing him to particularly grant a great amount of his personal favor to Akaza in comparison to his fellow Kizuki. As stated by Doma, that Muzan had tolerated and allowed Akaza's unique aversion to not eating or harming women and even only went as far as only dispatching him on special missions only, a privilege not even given to Upper Rank 1 or 2.
He was one of Muzan's favorites since he was loyal and serious.
During their interaction during the Upper Ranks meeting in the wake of Gyutaro and Daki's deaths, Muzan is shown to be just as annoyed, short tempered and degrading towards Doma as he is to the other Upper Ranks, where Muzan visibly expresses his anger, frustration, disappointment and withering faith in Doma due to his inability to live up to his expectation of finding the Blue Spider Lily and entombing and wiping out the Demon Slayer Corps and the Ubuyashiki Family for him.
Doma in turn has not displayed any form of fear, anxiety or anger at the Demon Lord despite his attitude towards him and the other Upper Ranks or any of the potential punishment he could inflict upon him, in fact Doma himself has not displayed the usual attitude of fear and respect most Demons show Muzan and is instead shown to take a more laid back and comedic disposition when interacting with him, as seen where Doma actually seems to be happy and excited on his potential "punishments" as seen where he enthusiastically offered Muzan if he should gouge out his own eye for him or perform any other form of extreme self harm to himself for the Demon Lord, further angering and annoying Muzan due to his enthusiasm and lack of seriousness/fear when interacting with him.
Muzan never really liked Doma, likely due to him noticing the latter's lack of emotions and desires.
Although their exact relationship was no seen, Enmu was known to have become powerful enough and famous in his exploits in battle to be recognized by Muzan as being a formidable enough to select him to become Lower Rank 1 and further augment his powers with his blood as a reward.
However upon Rui's death and defeat, Muzan was shown to have become completely displeased and repulsed by all of the Lower Ranks due to their apparent weakness in comparison to the Upper Ranks, earning the Demon Lord's ire and intense disappointment due to their apparent failure and contentedness not to advance in power due to becoming a Lower Rank. As seen during the Final Lower Ranks Meeting where Muzan showed obvious disdain for Enmu.
Enmu in turn was seen to harbor the utmost respect and admiration for Muzan despite his now hostile view of him and the other Lower Ranks, as seen where he was completely confident on Muzan's power and showed both pity and delight upon seeing Wakuraba's attempt to run away and knowing he stood no chance of surviving or escaping due to Muzan's extreme powers. Later as Enmu was the only surviving Lower Rank left, he expressed complete joy and ecstasy at Muzan's actions of slaughtering his fellow demons and even proclaimed that being killed personally by Muzan's hand was the greatest honor he could ever have in his life as a demon, showing just how intense Enmu's loyalty to him was.
Muzan in turn delighted by Enmu's words of adoration, decided to spare the Lower Rank and give him a chance to prove his worth and even went as far as giving Enmu even more of his blood and further augment and strengthen the demon's power to further assist him in his task. Again causing the demon further joy and happiness at the demon lord's "favor" and caused him to then decided to do everything he could to accomplish his mission in order to receive more blood to strengthen himself from the latter.
However, as seen from Akaza having appeared in the wreck of Enmu's Train after his attempt to devour humans in mass failed, Muzan likely did not have high expectations for him despite allowing sparing him and injecting him with more of his blood. This is seen where despite having Akaza stationed close to the train, he did not lend any assitance or back up to the Lower Rank and only entered into the battle after Enmu had been killed. Alluding that Muzan likely expected him to fail to begin with and ordered Akaza to follow him in secret to eliminate the demon slayers who successfully killed him when they are weakened from their battle against Enmu.
Although unknown when, how or why, Muzan became aware of and interested in Rui during his time as a human, specifically the fact that he was born as with a sickly and fragile human body that made even the simplest physical actions, such as walking, difficult and cause him to immediately collapse afterwards in exhaustion. Muzan, possibly empathizing with the young boy due to his own previous maladies and sickly body since birth, approached the weak young man and offered to "cure" him of his weak body, an offer Rui happily agreed to due to wanting to make his parent's happy and worry less for his health without fully knowing what Muzan was offering him. Muzan then gave him his blood and successfully transformed him into a Demon before once again leaving without telling him of the new characteristics and nutritional needs his new body, but nonetheless kept a close eye on the fledgling Demon's progress.
Eventually Rui like all Demons began killing people in order to survive, horrifying his parents who then attempted to kill their son before he could commit any greater atrocities but instead ended up being killed by Rui in self defense within their home. There, Muzan once again appeared before the young Demon who, was going through severe psychological shock and denial of his own actions. Realizing the fragility of Rui's mental state, Muzan proceeded to then manipulate the young Demon by telling him that the two dead humans killed at his own hands weren't his "real" family, "assisting" the young Demon's tormented and guilt-ridden mind by telling him to rationalize that his "true" family would never try to kill him and that he could simply search for a "new" family as a Demon. Eventually obtaining the young Demon's loyalty as a result of him "helping" him.
After these events, Rui continued killing and devouring humans and was eventually awarded with the position of Lower Rank 5 among the Twelve Kizuki, where Rui soon became something of a favorite of Muzan's. As seen where despite the Demon Lord's usual policy and law of preventing any Demons from banding and teaming up together in large groups, Rui was actually given special permission by Muzan to create his own "family" to satisfy his yearning for one, which then lead to the creation of the Spider Family. A privilege not even given to those of the Upper Ranks.
Initially, Muzan had considered Kyogai as a special Demon with an invaluable power due to his Blood Demon Arts, earning Muzan's favor and causing him to have high hopes for Kyogai's continued development as a demon as he grew stronger. Eventually causing the Demon Lord to give Kyogai the rank of Lower Rank 6 due to his abilities and possible powerful potential.
This in turn caused Kyogai to harbor a powerful sense of loyalty and admiration to Muzan due to him being the first person to truly "value" him for his talents and abilities and upon drinking a small amount of Muzan's blood and having his powers further enhanced, Kyogai respect for the Demon Lord only deepened due to realizing how mind blowing the amount of power he could obtain from him and took immense pride at him having been accepted by Muzan as one of the Twelve Kizuki. However upon Kyogai reaching his "limit" and gradually losing his ability to eat human flesh and grow stronger, Muzan was shown to have completely lost his original favor to the demon, coldly rebuffing Kyogai upon properly seeing his complete loss of appetite for human flesh despite his pleas for more time to prove himself and swiftly removed him from the position of Lower Rank 6 by cutting his digit rank from his eye.
Despite this horrible treatment, Kyogai is shown to still retain his admiration and loyalty towards the demon lord and has instead gone to extreme lengths to strengthen himself and grow his power despite already hitting his "limit" in order to once again reclaim his rank among the Twelve Kizuki by eating Marechi.