Macbeth has two major conflicts. The first is the internal conflict between his morals and his ambition, exemplifying the conflict of Man versus Himself. The second is the struggle between individual's evil interests, personified by Macbeth and Lady Macbeth; and the best interests of the nation, personified by Malcolm and Macduff, or the conflict of Man versus Man. Both conflicts evolve simultaneously throughout the rising action of the play.
Macbeth's internal conflict between his morals and his ambition begin with the witches' prophecies. Initially, he finds the witches' prophecies to be unbelievable, but when Ross greets him with the title Thane of Cawdor, which the witches had already prophesied, he wonders if he will have to commit a terrible act to fulfill the ambition the witches have planted. He struggles with this internal conflict throughout Act I and into Act II. The conflict is evidenced by the bloody dagger hallucination, his soliloquy and dialogue with Lady Macbeth, where she spurs him to commit the murder; and his mental breakdown after the murder, when he declares his hands will never be clean. This conflict resolves by Act IV, when Macbeth recognizes he does not deserve any of the benefits of old age.
The second conflict, ostensibly between Macbeth and Macduff, is an external conflict in which Macduff desires the best for Scotland and at no point believes that best to be Macbeth. Macduff shows his disdain for Macbeth by refusing to attend Macbeth's crowning and never dining at Macbeth's castle. The conflict escalates as Macbeth has Macduff's family killed while Macduff is England trying to gather forces to depose Macbeth. It then culminates in a one-on-one battle between Macduff and Macbeth, which Macduff ultimately wins.