How 'mad' is Hamlet? He certainly acts a kind of pantomime mad for Polonius and Claudius. But to his Mother he shows himself as very, very 'collected'.
Yet... he kills Polonius, talks to himself, and goes wild at Ophelia's funeral. He berates himself fiercely and is a whirlwind going nowhere.
What is your opinion of Hamlet's mental state? What would a psychiatrist say of his behaviour? He certainly acts mad, but does that mean he is sane underneath?
Well, that is one of the central questions of the play, isn't it--is Hamlet mad or mad in craft? It seems pretty clear that, at least at the beginning, Hamlet is play-acting. We know he is an actor who appreciates the art of acting, and he is probably just plying his craft for most of the play. He certainly seems sane enough when he says the words you quote above, which is actually fairly late in the play. IF something changes and Hamlet somehow crosses into the realm of insanity, it seems to me it happens when he realizes Ophelia is dead. He has to know he is to blame for her suicide, and his reaction is somewhat outrageous. At the end of his life, Hamlet appears to be lucid and almost resigned to his fate, indications to me that he is not suffering from any form of insanity.
I don't think he's truly crazy. I think that he is trying to use his so-called madness as a way to buy time. He is not really sure what he wants to do and/or what he should do. Given the situation he's in, acting like he's crazy is actually a pretty good idea. He can act crazy to cover up his anger towards Claudius and Gertrude and life in general until he figures out what he should actually do.
Hamlet is certainly not in a good place mentally. His first words are explaining to his mother and step-father that he is in the grip of deep grief over the death of his father (and the lack of grief shown by his mother). Then the 'I have of late...' speech is a spot on description of acute depression. And, of course, he comes perilously close to killing himself. Are these things madness? I am not a psychiatrist, but I would say that for the first two thirds of the play Hamlet is fast approaching a nervous breakdown, despite the 'acting mad' stuff. In the last section of the play, after his return from his aborted trip to England, he seems much colder and resolved. He has given in and let go of his dreams of beauty and truth and become less emotional.
Hamlet is not a lunatic, but he is falling apart mentally until he cauterises all his emotions.