Perhaps the world's most famous mental patient, Hamlet's sanity has been argued over by countless learned scholars for hundreds of years. As a mere student of advanced-level English Literature, I doubt I can add anything new to the debate in 2000 words, but I can look at the evidence supporting or dispelling each argument and come to my own conclusion.
Hamlet is obviously experiencing grief and despair right from the beginning of the novel, with the death of his father and his uncle's seizure of the throne and rapid weddign of Hamlet's mother, and we can observe his great grief bordering on irrational suicidal tendencies as early as Act II Sc I, where he gives his first soliloquy. He cries:
"O that this too too solid flesh would melt,
Thaw, and resolve itself into a dew!
Or that the Everlasting had not fixed
His canon 'gainst self-slaughter!"
Macbeth wants his flesh to dissolve into a dew ("solid" contrasting with "melt" in the first line), and wishes that God had not forbade suicides from going to heaven. This is also the first glimpse of another recurring theme in the play, that of Hamlet's unhealthy obsession with the afterlife. This is one of the reasons that the ghost of his father has such an effect on him, which is a trigger for all the subsequent events in the play.
Moving on to the fourth scene, the next interesting speech is on l. 23. It is a long and complicated speech, but its general gist is that if a person has one fault, no matter how virtuous they may be in other ways, they are soiled by "the stamp of one defect". This speech is quite ironic, because it is Hamlet's "one defect" (his hesitancy and inability to take action), regardless of his other qualities (such as honour and integrity), will be the main reason why the play ends so tragically.
Although we are supposed to suspect that "something is rotten in the state of Denmark", as Horatio puts it, from the start of the play, it is only when Hamlet talks with the ghost of his father in Act I Sc V that we realise the full extent of his uncle's treachery. When he first sees the ghost, Horatio and Marcellus try to restrain him, Horatio saying:
"What if it tempt you toward the flood, my lord,
Or to the dreadful summit of the cliff
That beetles o'er his base into the sea,
And there assume some other horrible form,
Which might deprive your sovereignty of reason,
And draw you into madness?"
Horatio is afraid that the ghost will get Hamlet to follow him to a cliff hanging over the sea, and then change into some other apparition, making Hamlet lose his mind and his sovereign power of reason. These words are very ironic, for as a result of seeing the ghost and hearing the dreadful truth about his father's murder and mother's adultery Hamlet says he will put on an "antic disposition", telling the others that he will act oddly, but that they musn't tell anyone why he is doing so. Hamlet has already told us that he is a man of thought rather than action (earlier in the play he says that Claudius is as different to his father "as I to Hercules"), and he is going to act oddly so that the King doesn't suspect Hamlet is plotting his downfall. However, Horatio and Marcellus even now think that Hamlet is acting rather strangely, saying "These are wild and whirling words, my lord", and "this is wondrous strange".
The next passage of interest is in Act II Sc II, when Claudius says to his Rozencrantz and Guildenstern:
"... Something have you heard
Of Hamlet's transformation; so call it,
Since nor th' exterior nor the inward man
Resembles that it was."
Claudius is keen to talk of Hamlet's rumoured madness, because he thinks Hamlet might know something about his treachery and wants to deflect his guilt and detract from Hamlet's credibility. To the audience, who have already heard the ghost's...