Claudius and Gertrude greet Hamlet's old friends Rosencrantz and Guildenstern, whom they summoned to Elsinore to figure out why Hamlet is so melancholy. Rosencrantz and Guildenstern happily agree to help.
R and G are introduced. They never see through the various plots and are manipulated by everyone.
Polonius enters and says that he has figured out the cause of Hamlet's lunacy. But, first, the ambassadors have returned from Norway. He goes to get them. While Polonius is gone, Gertrude remarks that Hamlet's mania probably comes from his father's death and her too-hasty marriage to Claudius.
Some critics wonder at whether Gertrude was complicit in Old Hamlet's murder. But her comment here indicates she's unaware that Claudius murdered Old Hamlet.
Polonius returns with the ambassadors. They report that the King of Norway rebuked Fortinbras, who promised not to attack the Danes. Norway then rewarded Fortinbras by letting him attack the Poles. Now Norway asks that Claudius give Fortinbras' army free passage through Denmark on the way to Poland. Claudius agrees. The ambassadors leave.
Fortinbras agrees to give up his effort to revenge his father and seek honor in another way. Is his promise reality, or appearance? Has Claudius just allowed a hostile army to march into his country?
After a long-winded ramble about Hamlet's madness, Polonius reads love letters Hamlet sent to Ophelia. Claudius and Gertrude agree that lovesickness may be causing Hamlet's behavior. Polonius proposes that they stage a meeting between Hamlet and Ophelia and spy on it to test his theory. Claudius agrees.
Polonius comes up with another plot to try to find out what's really bothering Hamlet. Polonius once again is willing to use Ophelia in that plot.
Hamlet enters, reading. The King and Queen leave Polonius alone to talk with him. Polonius speaks with Hamlet, who responds with statements about pregnancy, death, and rot that, though nonsensical, also seem to refer to Denmark, Ophelia, and Polonius. Polonius, perplexed, exits.
Hamlet speaks in prose here, representing his "madness." But Hamlet uses madness only to mock Polonius, not to seek revenge.
Rosencrantz and Guildenstern enter. Hamlet greets his old friends warmly, and tells them that Denmark is a prison. They disagree. Hamlet responds, "then tis none to you; there is nothing either good or bad but thinking makes it so" (2.2.245-246). He launches into a long speech about the beauty of the world and nobility of man, all of which looks to him like dust and fails to delight him.
Hamlet wants the world to delight him, but he knows things (such as the fact that his father was murdered) that make its beauty meaningless, a lie. And if life is pointless, what's the point of seeking revenge?
Hamlet asks why they've come. They say to visit him, but Hamlet angrily demands whether they were summoned by the King and Queen. Rosencrantz and Guildenstern admit they were.
R and G are dupes, acting without any understanding—they're the opposite of Hamlet, who understands too much.
Hamlet cheers up a little when Rosencrantz mentions the arrival of a troupe of players (actors). Hamlet says his "uncle-father and aunt-mother" are wrong: he's only insane some of the time (2.2.359).
Actors make appearance seem like reality for a living.
Polonius enters with the players. Hamlet mocks Polonius, but greets the players warmly. He asks the First player to act a speech about the Trojan queen Hecuba's grief at the death of her husband, Priam. The Player does, with great feeling.
Priam was killed by the Greek Pyrrhus, who was getting revenge because Priam's son, Paris, killed Pyrrhus's father, Achilles.
Hamlet tells Polonius to treat the players well and give them good lodgings, and privately asks the First Player to perform The Murder of Gonzago on the following night, with some extra lines Hamlet will insert himself. The Player agrees.
It's interesting that Hamlet, who is so obsessed with what is real, feels so comfortable with actors, whose job is to make the unreal seem real.
Alone, Hamlet is furious that the Player could get so emotional over long-dead Hecuba, while he can't even bring himself to revenge his murdered father. Hamlet muses on a plan he's come up with: he'll have the players show a scene similar to Claudius's murder of his father: "The play's the thing wherein I'll catch the conscience of the King" (2.2.582).
By condemning himself for not acting and then plotting to use the play to determine Claudius's guilt, Hamlet reveals his fear that Claudius might not be guilty, that the Ghost might be lying. Hamlet has a reason for his inaction: lack of evidence.