Like all good characters, villain or otherwise, the Master is a complex person with many layers to his personality. In his role as villain, the Master reveals a very callous nature, often either indifferent to or openly amused by the suffering of others. He can be cold-blooded, killing without remorse. The Master believes that his goals are more important than the well-being of those around him. Anyone standing in his way has, in his eyes, chosen to become a target. The Master is mostly amoral, believing more in cause and effect, than right and wrong. To him, right and wrong are subjective labels that people use to judge each other, based on their own biases.
The Master's lack of morals is, however, not a lack of standards. The Master, except in extreme circumstances, is polite and well-spoken. He is the type of villain who will hold a door for a lady, while on his way to kill someone. His behavior is only rarely coarse or crude. The Master is well versed in the social graces and can be quite likable. He possesses a great deal of charisma.
The tragedy of the Master is that he's a character who possesses a vast potential for good, if it weren't for his corrupt philosophies and goals. The Master also suffers from insanity. He has been tormented by drums, pounding in his mind, since he was eight years old. By the time he steals Tremas's body, his mental condition has deteriorated a great deal. This is sad, since parts of his canon, Yana especially, reveal that the Master is capable of being greatly and genuinely kind, when he is in his right mind. There is part of the Master that yearns for a life of more than just the hunt for power. Part of this is a yearning to be reunited with his estranged friend, the Doctor.
The Master's interactions with the Doctor reveal that, good manners and villainy both aside, the Master has a very playful personality. He enjoys dressing up in disguises, doing so even when it is not necessary. The Master's traps for the Doctor are so overly complicated that they seem more designed to challenge the Doctor, than to harm him. The Master certainly takes a delight in his rivalry with the Doctor, praising him as an intellectual near-equal. Even the Doctor admits that killing him isn't the Master's first priority. He derides the Master's threat to kill him in the Death Zone, saying, "And not humiliate me first? Oh, that isn't your style at all." Despite his lack of morals, the Master does have a personal set of rules that he strays from only reluctantly.
The Master's relationship with the Doctor is very important to the character. They were, at the least, very close friends, while growing up together on Gallifrey and attending the Academy. While their relationship tends to shift, it is always intense, whether they are friends, best enemies, rivals...or lovers. The Master is very much in love with the Doctor, even though he feels compelled, at times, to kill him, knowing the Doctor is really all that stands between him and his goals. The Master is unsure of the Doctor's feelings and this makes him resentful. Still, he can't quite bring himself to kill the Doctor, because, "a cosmos without the Doctor scarcely bears thinking about."
However, the Master is capable of forming other relationships. We learn in Trial of a Time Lord that the Master has a long standing business relationship with Sabalom Glitz. In Logopolis, the Master tries to tie Nyssa to him. He pretends at first to be Tremas and gives her a bracelet so he can control her. At one point, he even threatens to leave and orders her to accompany him. He has more than one romantic alliance with women, Lucy Saxon and Galleia, though he seems to be using them, at least to an extent. Still, the Master is capable of emotional attachment.
Mostly, the Master is a creature of extremes. He both loves and hates very intensely, sometimes feeling both for the same person. He is very energetic and driven. Unfortunately, his emotions are often expressed with acts of villainy or violence. Nevertheless, he is far from a cartoon villain and can be calm, even kind, when it suits him. Far more than a simple psychopath, the Master can be frightening, funny, sincere, and/or deceptive, at any given moment.