The play does not, strictly speaking, adhere to either Aristotle's unity of time or place. The play takes place over several months rather than during the course of twenty four hours. It begins less than two months after Hamlet's father's death and less than one month since his mother's remarriage to his uncle—his father's brother—Claudius. Hamlet feigns madness, hires the players to act a scene like his father's own death, leaves for England, and returns to Denmark, etc., over the course of the next couple of months.

Further, action takes place within different rooms in the palace at Elsinore, as well as in the cemetery where Ophelia is buried, and on the castle ramparts where the dead king's ghost is seen. For these reasons, this play does not adhere to either Aristotle's unity of time or place.

The idea of unity of time and unity of place comes from Aristotle's Poetics. In discussing the difference between an epic and a tragedy, Aristotle defines unity of time, place, and action. 

In Poetics, Aristotle says epics and tragedies differ. While epics can cover long periods of time and are set in many different places, tragedies should have unity of time and place. The events of a tragedy, ideally, should "as far as possible, confine [themselves] to a single revolution of the sun." Obviously, the events of Hamlet take more than 24 hours, but when compared to the Epic of Gilgamesh or The Odyssey, Hamlet's timeline is not unbelievably long to an audience watching the play.

In addition, the action of a play should all take place in the same general physical setting. At it's most extreme, this looks like Oedipus Rex, where all the action of the place takes place outside the castle. Anything that happens away from that setting is not shown by the actors, but related through the dialogue. In Hamlet, most of the action is in or around the royal court in Elsinore, Denmark. When Hamlet goes to England, for example, the audience doesn't see any of that; they just hear about it afterwards, back in Denmark. In this way, Hamlet has unity of place as well.