Hamlet's cray-cray behavior is no news to Claudius. In hopes of finding out what's going on with Hamlet, Claudius and Gertrude have invited two of Hamlet's school friends to Denmark. Rosencrantz and Guildenstern, whom Claudius can't tell apart, promise to report back to the King and Queen with any information they can gather.
Apparently, spying on your children is the thing to do around Denmark.
Speaking of people who spy on their children, Polonius enters. He claims he has found the source of Hamlet's madness, but first, the King really ought to meet his ambassadors.
Voltimand and Cornelius enter, fresh from their Norwegian expedition. Turns out that Claudius is a successful diplomat; he has avoided war with Norway after all. Young Fortinbras (remember him from Act I, Scene i?) has promised his uncle (the current king of Norway) that he'll behave. Fortinbras further says he won't plot to destroy Denmark in order to take back the lands his dead father lost in a bet.
Once that's out of the way, everyone gets back to the moody young Hamlet business. Polonius informs Claudius and Gertrude that Hamlet has been driven mad by love for Ophelia. To prove his point, he reads some love letters that the Prince wrote about how sexy she is (seriously —an "excellent white bosom").
They decide to...spy on their children. Specifically, they plan to set up a meeting between Hamlet and Ophelia, in the location where Hamlet has taken to pacing insanely, and watch what happens.
The King and Queen give the plan the go-ahead and, seeing Hamlet coming, they quickly rush out of the hall.
Hamlet comes in, deliberately misunderstands Polonius' questions, and says things that seem to be irrelevant. But are they?
Polonius first asks if Hamlet recognizes him, and Hamlet replies he knows him as a "fishmonger" (that's a guy who sells fish). When Polonius says he's not a fishmonger, Hamlet essentially says that's too bad. He wishes Polonius were someone as honest as a man selling fish. Maybe because a fishmonger is up to one thing, selling his wares, whereas Polonius is clearly scheming at the moment and not being straightforward with Hamlet.
Hamlet also quips that honest men are rare in this world, something Polonius agrees with.
Next, Hamlet moves on to a confusing bit about how the sun isn't particular about who it shines on. The sun, he says, would breed maggots in a dead dog because even that flesh is good enough to be "kissed" by the sun. Okay, so Hamlet's pretty down on the world and also quite intent on confusing the bejeezus out of Polonius. He changes subjects quickly by asking if Polonius has a daughter. Polonius confirms this, and Hamlet replies that even though "conception," as in understanding, is a good thing, "conception," as in getting pregnant, wouldn't be such a good thing for Ophelia. He's making fun of Polonius in two ways here: for not getting what's really going on, and for being crazy over-protective of his daughter.
Polonius, who continues to not get it, can only focus on the fact that Hamlet has mentioned Ophelia. He takes this as a sign that he's on the right track and that it is indeed Hamlet's love of Ophelia that is driving him mad.
Polonius asks what Hamlet is reading, and Hamlet says his book is about how foolish and disgusting old men are. Hamlet says that while he agrees with the assessment (a direct insult to Polonius), he doesn't think it's very nice that someone wrote it down. He adds that after all, Polonius would only be as old as Hamlet...if time went backwards. (If you want to watch a master at work, watch David Tennant—of Doctor Who and Jessica Jones fame—deliver these lines.)
Polonius is starting to see that Hamlet is speaking in double entendres.
Then, Polonius suggests Hamlet should take a walk "out of the fresh air," which Hamlet obviously uses as an opportunity to say he'd like to walk out of the fresh air and into his grave.
Polonius again sees that Hamlet is engaging in some wordplay here, but he doesn't fully understand what's going on. He decides the best thing to do is to proceed with the plan to send Ophelia to talk to Hamlet and spy on them to see what happens.
Polonius offers to take leave of Hamlet, and Hamlet replies no other loss would make him happier, except the losing of his life.
As Polonius is leaving, Hamlet dismisses him as a tedious old fool: he's fallen into Hamlet's trap of making everyone think that he's mad.
Hamlet, says he'll make it easy for them: everything sucks, and neither men nor women "delight" him.
Rosencrantz has a bit of a giggle when Hamlet declared that men don't delight him, and Hamlet wants to know what's funny.
Oh, it's just that there are a bunch of actors heading to the castle.
Why are they traveling? Hamlet wonders. Are they not as well loved on their home turf as they used to be?
By way of explanation, Rosencrantz indulges in some theater gossip.
History Snack: This entire passage is an allusion to Shakespeare's day, an era when public theaters were shut down during times of instability—like when the plague got a bit out of control or when there was a civil disturbance.
Rosencrantz says the actors are likely on the road because of a recent innovation, a.k.a., children's plays.
NOTE: Plays with child actors were all the rage in England at this time, which forced theater troupes featuring adults to take their shows on the road. Shakespeare was on the grown up actors' side, and is making a little jab at the children's plays, especially when Rosencrantz refers to child actors as "little eyases" or, little hawks.
Shakespeare takes the chance to make fun of the folks that support the children's plays in Elizabethan England by having Hamlet compare child-play supporters to the men that used to make stupid faces at his Uncle Claudius, and now pay big money for little pictures of him.
Their conversation comes to an end when the players arrive.
Before talking to the players, Hamlet tells Rosencrantz and Guildenstern that they are welcome to hang out, but that Hamlet's "uncle-father and aunt-mother" are deceived.
Guildenstern says something along the lines of, "About what?" Then Hamlet makes the comment that he's only mad if the wind blows north-north-west, because otherwise he knows a hawk from a handsaw.
This wind/hawk/handsaw business is another one of Hamlet's crazy comments about not being crazy that pretty much makes everyone else think he is, indeed, losing it.
When Polonius comes in, Hamlet mocks him openly, making fun of the fact that Polonius is coming in to tell him something he already knows: that the actors have arrived. When Polonius says he has news, Hamlet says, "So do I," and then begins to relate a bit of news so old it's about Roman times. Of course, Polonius's news isn't that old, but still, Hamlet's having fun at his expense and it goes right over Polonius's head.
In fact, Polonius doesn't understand anything Hamlet says until Hamlet starts calling him Jephthah, judge of Israel. Jephthah is a character from Judges 11, of the King James Bible, who inadvertently offers up his only child, a virgin girl, as human sacrifice in exchange for winning a battle. And when Polonius picks up on that, he again thinks that Hamlet is still obsessing over Ophelia. Hamlet sure knows how to push Polonius's buttons.
But when the players (a.k.a. actors) arrive at the castle, Hamlet is actually super excited to see them.
He asks for a speech he once heard performed; he thinks it was performed no more than once, because the vulgar masses couldn't appreciate it, though he and the critics did. (Hamlet's telling us here that he has a fine artistic sensibility, and a penchant for poetry, unlike the groundlings or, common folks that sat in the cheap seats at plays.)
What speech? It's the tale Aeneas told Dido about Priam's murder, all drawn from Virgil's Aeneid. It's a significant story because Pyrrhus, son of the warrior Achilles, comes to Troy in the Trojan horse to avenge the death of his father by killing Priam, King of Troy.
Hm, a son killing a king to avenge his dad?
The speech details Pyrrhus's dark, scary, blood-covered rage. Then we get to Hecuba, Priam's wife, who's pretty upset by the whole thing.
Hamlet starts reciting the speech himself, then lets an actor take over. The actor gets so worked up by the description of Hecuba's emotion at her husband's death that he has tears in his eyes.
Polonius, meanwhile, is super bored, since he only likes the bits with dancing and sex.
Hamlet then has a private confab with the main actor, asking if they can perform The Murder of Gonzago for the court tomorrow night—with the little addition of a speech that Hamlet will write himself. The player agrees. (Hamlet is the prince, after all.)
Left alone, Hamlet berates himself for not yet having avenged his father's murder, in one of the most famous soliloquies... ever. He basically asks how the actor can weep for a fictional character, while he himself does nothing about his own father's very real death.
Hamlet calls himself a coward and a promiscuous woman (seriously) for not having acted on the ghost's revelation. Beyond his cowardice, he's ashamed that even when Heaven and Hell would have him take revenge, he can only prance about and whine.
One thing that's holding him back is the fear that the ghost was lying—since, sometimes the devil takes a pleasing shape to ease a worried mind.
Hamlet decides to have the actors stage a version of his father's death in front of Claudius so he can watch Claudius' reaction.
If Claudius flips out, Hamlet can rest assured that he's guilty.