How does Hamlet work to examine human behavior and psyche, and what role does Act V play in establishing this depth/connection? Why is Hamlet so often referred to as Shakespeare's (and literature's) greatest achievement and how is Act V the crowning moment?

Hamlet examines human behavior and the psyche in several different ways. One is by its portrayal of madness. Hamlet announces that he will feign madness, but his behavior, as well as several of his soliloquies, suggest that his madness may be authentic. He experiences bouts of melancholy, expresses uncontrollable rage, and generally behaves erratically throughout the play. The characters in the play are generally convinced that he is insane, and the audience is forced to contemplate the fine line between madness and sanity as part of the human condition as well as in the title character. Beyond this, we encounter in Hamlet a character wracked by self-doubt, a trait most people can identify with. At times he doubts himself capable of avenging his father's death and continues to stall throughout much of the play. He declines, for example, to kill Claudius when it would have been very easy to do so, citing the fact that his uncle is praying. His tortured relationship with his mother and with Ophelia (whose own decline into madness also suggests the frailty of the human psyche) show him to be a intensely conflicted character. Act V is in many ways the crowning achievement of the play, as the audience witnesses a resolution to the conflicts between Hamlet and Claudius, Hamlet and his father's ghost, and Hamlet and himself. The first scene of the act witnesses Ophelia's tragic death and Hamlet's extended and melancholy speech on mortality (occasioned by his discovery of Yorick's skull). The second scene closes the play with the death of Claudius and Hamlet, whose vacillations in seeking revenge give way to focus as he kills his uncle.