Enter King, Queen, Polonius, Ophelia, Rosencrantz and Guildenstern:
As the scene opens the King is questioning Rosencrantz and Guildenstern about why Hamlet "puts on this confusion." Rosencrantz and Guildenstern don't have any satisfactory answers. Hamlet admits that "he feels himself distracted," Rosencrantz says, "But," Guildenstern adds, "with a crafty madness, keeps aloof" (3.3.8). By calling it a "crafty madness" Guildenstern is almost certainly not suggesting that Hamlet is only pretending to be mad. He means that in his madness Hamlet is wary and shrewd.
Neither one mentions that Hamlet has figured out what they are up to. Are Rosencrantz and Guildenstern embarrassed to appear so stupid, or are they just plain stupid? It's hard to tell.
Like a mom, the Queen seems interested in her boy's behavior and happiness. She asks if Hamlet acted like a gentleman, and if they encouraged him to take part in any "pastime." Rosencrantz replies with the news about the players, and Polonius adds that Hamlet has invited the King and Queen to see the play. The King agrees to that, and sends Rosencrantz and Guildenstern on their way to encourage Hamlet to go ahead with his plans for "these delights."
Exeunt Rosencrantz and Guildenstern:
This famous soliloquy may be a surprise. A few minutes ago, in his second soliloquy, Hamlet had beat himself up for not taking revenge against the King, and then he had explained to himself that "the play's the thing / Wherein I'll catch the conscience of the king" (2.2.604-605). So he had a plan. But now he seems to have forgotten all about his plan. Instead, he's feeling very much as he did in his first soliloquy, when he wished that his "too too solid flesh would melt / Thaw and resolve itself into a dew! (1.2.129-130).
At first, "to be, or not to be" doesn't mean "to live or die." It's a question of whether to "suffer / The slings and arrows of outrageous fortune" or to "take arms against a sea of troubles." "Suffer," in Shakespeare's time, means primarily to "allow" or "permit," so Hamlet is talking about just letting things happen without doing anything. This is what it would be to "not be," but the other option, "to take arms against a sea of troubles," doesn't look much more hopeful. What good would a sword or spear do against a sea? Then Hamlet thinks of the ultimate solution, to "not be" at all, "To die, to sleep." For a moment, he seems to fall in love with this possibility. He says that "'tis a consummation / Devoutly to be wish'd," and there's a lullaby quality in the rise and fall of his next words: "To die, to sleep; / To sleep: perchance to dream" (3.3.60-61).
As he says these words, Hamlet--as Hamlet tends to do--hears himself thinking, which makes him think another thought. That other thought is that the sleep of death may not be comforting at all. (The Ghost has told him that the experience of purgatory is terrifying.) He says, "there's the respect [thought] /That makes calamity of so long life" (3.1.68-69). In other words, even if our life is a total calamity, we'll prolong the calamity, rather than face the unknown of death. Otherwise, says Hamlet, who would endure all of the common pain and agony of life, when he might solve all of his problems with a "bare [mere] bodkin [dagger]"?
Again, Hamlet hears himself thinking, and says, "thus the native hue of resolution / Is sicklied o'er with the pale cast of thought" (3.1.84-85), meaning that if he had been decisive enough to solve his problems, it's too late now, because thinking makes healthy decisiveness sick. Taken altogether, this soliloquy seems to float away from the context of the action. There's nothing specific in it about his father, or his mother, or the King, or anything that Hamlet has done or failed to do. He expresses a desire for death, and a fear of death, and scorn for himself for thinking himself out of actually doing anything. He seems overwhelmed, but it's hard to see what--other than his own thoughts--is overwhelming.
Hamlet sees Ophelia:
Ophelia has a little surprise of her own. After greeting Hamlet, she says, "My lord, I have remembrances of yours, / That I have longed long to re-deliver; / I pray you, now receive them" (3.1.93-95). "Remembrances" could be love-letters, or pressed flowers, or any little gifts that a man might give a woman because he likes her. They can't be the book that Polonius gave Ophelia to "color [her] loneliness." So Ophelia has gone far beyond what her father has asked of her, which was just to be where Hamlet would find her. Hamlet says "I never gave you aught," which we must take to mean "I never gave you anything that you need to return," since we know that he did give her the love-letter that Polonius read to the King and Queen. Ophelia then says that he should take "these things" back because he doesn't love her anymore, and "Rich gifts wax poor when givers prove unkind" (3.1.101).
What's Ophelia up to? Does she consider his silent visit "unkind"? Or does she hope that he will tell her to keep the remembrances because he really does love her after all? In any case, she completely ignores the fact that she was the one who dumped him, and this seems to be what makes Hamlet say "Ha, ha! are you honest?"
At first, Hamlet seems to be simply asking if she really believes what she's saying, but her "My lord?" seems to show that she doesn't understand the question. So there she is, a beautiful woman for whom he has (or had) strong feelings, either lying or blind to the way she is twisting the truth. When Hamlet absorbs this, he changes the way he uses the word "honest." He tells Ophelia that her "honesty should admit no discourse to [her] beauty" because "the power of beauty will sooner transform honesty from what it is to a bawd than the force of honesty can translate beauty into his likeness" (3.1.111-114). Now Hamlet is using the word "honest" to mean "chaste" and he means that beauty can be a pimp. He adds, "this was sometime a paradox, but now the time gives it proof." He's probably referring to his mother, whose beauty attracted Claudius, so that she changed from an honest wife to King Hamlet into (in Hamlet's eyes) King Claudius' whore.
After this outburst, Hamlet tells Ophelia, "I did love you once." In what follows, the words are clear, but Hamlet's emotional tone is not. As soon as Ophelia says "you made me believe so," he says "I loved you not." "Get thee to a nunnery" (3.1.121) he advises her, because there she'll be safe from men, who are all--himself included--"arrant knaves." Hamlet could be sarcastically throwing her own dishonesty in her face, by telling her he's just as bad as she is, or he could be tenderly attempting to get her to protect herself from a harsh world.
Now there's another twist. From out of the blue--as when Hamlet asked Rosencrantz and Guildenstern if they were "sent for"--Hamlet asks Ophelia, "Where's your father?" Movies of Hamlet often give the prince a clue for this line, by showing him spotting a shoe or a pair of eyes, but it seems more likely that Hamlet simply intuits the truth that Ophelia's very presence is a lie, and that he's being spied upon.
Poor Ophelia naturally lies, saying "At home, my lord," and Hamlet explodes in rage. Twice he says, "Farewell," but thinks of something more to say, and turns back to heap more abuse upon Ophelia. He calls Polonius a "fool," and speaks to Ophelia as though she is all deceiving women: "Or, if thou wilt needs marry, marry a fool; for wise men know well enough what monsters you make of them" (3.1.138-140). He tells her again to get herself to a "nunnery," but this time he's probably using the word in its slang sense of "whorehouse." Finally, he's really ready to leave, but not before issuing a threat:
Enter King and Polonius:
Meanwhile, the King has seen quite enough. He is pretty sure that Hamlet is not in love and not mad, and that "There's something in his soul, / O'er which his melancholy sits on brood" (3.3.163-164). Of course, the King Claudius knows that the "something" could very well be the murder of King Hamlet, and that Hamlet could be dangerous. He tells Polonius that he has determined to send Hamlet to England "For the demand of our neglected tribute," because a sea voyage will be good for Hamlet's mental health. Polonius, however, will not let go of his idea that Hamlet's problem is "neglected love," so he proposes a new scheme, which is to "Let his queen mother all alone entreat him / To show his grief" (3.1.182-183), while Polonius again hides and listens in. The King replies "It shall be so," but we don't get the idea that he's changed his mind about getting rid of Hamlet.