Francisco and Bernardo show Horatio the ghost of the King Hamlet. They get King Hamlet's son, Hamlet to show him the ghost because the ghost won't talk to them!
The ghost takes Hamlet to a quite spot and tells him that his uncle Claudias, who is now King and is married to the ghost's old wife, Gertrude, had murdered him by dropping poison in his ear and it wasn't a snake. Hamlet wants revenge.
Hamlet promises revenge and tells Horatio, Bernado and Fransisco and also tells them not to tell anyone else. Hamlet tells them that he wants revenge by acting like he has gone mad.
Meanwhile, over in Denmark, Polonius and Leartes have heard from Claudias that Hamlet has gone mad so they tell Ophelia, who is Hamlet's girlfriend and Polonius daughter and Leartes sister, that she can't be with him and Hamlet doesn't love her. She is heart broken.
Just to ensure that Claudias is guitlty, Hamlet puts on a play reanacting the murder of his father. He wants to see how he reacts and if he his bothered by it.
Hamlet has caught Claudias out but he still acting mad. Claudias asks some of Hamlet's childhood friends to keep an eye on him. Polonius thinks that Hamlet is going mad for love for Ophelia so allows her to see him.