Hamlet is not every truly mad; he clearly states that he plans to put an "antic disposition" on and he successfully does that in several subsequent scenes. I do think the entire situation is maddening to him -- he is outrages over the marriage and the murder, and overwhelmed by the task of revenge, but he never loses his mind. As for the issue of not losing his soul in the act of a murder, I don't think Hamlet would see the death (murder) of Claudius as a murder -- it is an act of justice. While he clearly has reservations, that explains his delay and his need for "proof" of the ghost's story. In regards to Rosencrantz and Guildenstern, I think those deaths fall under the category of "self-defense." Once he knows that content of the letter he has to do something in the name of self preservation! He chooses himself over them!
Great points made above, but these answers do not explain, if murder is a mortal sin, why Hamlet then condemns his own soul by murdering or causing the murder of Polonius, Ophelia (who really does go mad) and Rosencrantz and Guildenstern?
The whole delemma for Hamlet, as I see it, is to revenge his father's murder and somehow not lose his soul in the process. If he is not "mad" when he committs these actions that lead to various deaths, temporary insanity, perhaps, he loses his soul.
I would like to think that flights of angels do accompany him.
I don't think any part of Hamlet's behavior shows true madness. I think that he is just an indecisive person who is trying to cover his confusion and anger by pretending to be mad. He is acting that way, for example, so that he can chastise his mother for marrying her husband's killer.
I think that Hamlet keeps "winking" at the audience, telling us he is not mad. We see that most clearly when he says that he can tell a hawk from a handsaw if the wind is blowing in the right direction.
I don't see evidence of true madness in Hamlet -- I think he's feigning it all the time.
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As to the question of how much of Hamlet's madness is feigned, in Shakespeare's play, Hamlet, this is a long-standing debate.
However, in my opinion, I believe most of it is feigned, especially in the company of specific characters in the play. With Ophelia, I believe Hamlet is acting most of the time, but a part of him that cares for Ophelia is probably only slightly "hysterical" rather than pretending madness. For the part of Hamlet that believes Ophelia simply a pawn of the King and her father, I think he turns the crazy act on and off at will, knowing she will take the news of his behavior back to both men.
Part of me wants to chide the Dane because he never gives Ophelia a chance to take his side. However, the part of him that does not want to believe she would turn her back on her feelings for him probably drives him to higher levels of frustration, as seen in his "get thee to a nunnery" scene with Ophelia.
With Claudius and Polonius (as well as Rosencrantz and Guildenstern, who are merely buffoons), Hamlet is a "dumb as a fox," which means he is well aware of what is going on with these men: they are trying their best to figure out what is eating Hamlet.
Claudius would fear it is knowledge, somehow, of his uncle's murder of Hamlet's father.
Polonius, a foolish old man, simply wants to be in the royal family's inner-circle, so he insists Hamlet's behavior is all about Ophelia; this is Polonius' ticket to remaining close to the King.
Rosencrantz and Guildenstern are puppets of the King, and Hamlet has no time for them.
In all three of the above instances (involving the men), Hamlet's pretended madness is to not only throw them off of his "scent" in the "hunt" between Claudius and Hamlet, but it also allows Hamlet to insult them all, making it seem like he has a "fevered brain." It's all a little childish on Hamlet's part, for none of it brings him any closer to fulfilling his promise to his father's ghost of avenging Old Hamlet's murder.
With Gertrude, I think Hamlet starts out acting crazy when she is with Claudius, but in Act III, scene iv, when Hamlet kills the spying Polonius in his mother's chambers, I think he finally is truthful with her, and with eyes partially opened, I believe she sees what is really ailing her son: a broken heart, not a broken mind.
Hamlet doesn't ever seem crazy to me when he is alone. He is philosophical, and even rants at his inability to act, as well as the lunacy he sees around him, but he always seems more frustrated and aggravated than crazy.
Hamlet's famous speeches, "To be or not to be," and "What a piece of work is man," demonstrate a strong grasp on reality, though a grasp that is shadowed by loneliness for the task before him, melancholy at the loss of father and (seriously, in his mind) his mother, and disappointment in others, especially Ophelia. It is hard, too, for him to see the extent of evil in a man's soul, particularly Claudius.
Hamlet puts on an "antic disposition," just as he declares he will after learning of his father's murder. There is "a method" to his madness, and the rest is simply the human suffering of a once-gentle son and sweetheart.
When Shakespeare writes a character going mad, he switches from iambic pentameter to prose. Read in your text Hamlet's speech and determine what looks like Shakespeare and what looks like it could appear on the pages of a novel.
The prose is madness, the iambic pentameter is the sign of a sound mind.