Macbeth's main conflicts are tied to Duncan's murder. The initial struggle is internal, as macbeth is torn between ambition and his understanding of right and wrong.
Another conflict arises in the relationship of Macbeth and Lady Macbeth. She encourages her father's murder, tells Macbeth he's a coward, and then names his feeling of guilt weakness.
Lastly, there's the conflict between Macbeth (interested only in himself) and Malcolm and Macduff, who support the collective interests of the nation.