How does Hamlet change throughout the play?

Hamlet is depressed and grieving as the play starts because he has just lost his father. However, his depression and disillusionment take a sharp nose dive when he meets his father's ghost and learns that his father was murdered by his brother Claudius, Hamlet's uncle and the new king.
The world appears to Hamlet a dark, diseased, and corrupt place where nobody can be trusted. He feels suicidal. He pretends to be crazy to keep the courtiers around him, whom he doesn't trust, off kilter. However, by the time he confirms that Claudius is the killer and confronts his mother about why she married him, Hamlet is in such a frenzy that he seems to have fallen into a genuine fit of madness. During this fit, he may or may not see his father's ghost again, and he murders Polonius, mistaking him for Claudius.
Hamlet experiences anguish and despair over the meaning of life and his place in the world over the course of the play. He confronts radical evil and recoils from what he sees. However, by the end of the play, he has regained some equilibrium. He kills Claudius and, as he is dying, begs Horatio to stay alive to tell the story of what happened.
In brief, we could say that Hamlet moves from a naive view of life to one that is fully aware of evil in the world.