In act 1, the castle guards meet with Horatio late at night on the castle ramparts because they want him to witness the ghost they have seen. He at first pooh-poohs the idea of the ghost, but he is convinced when he sees it with his own eyes. He also tells them that all the war preparations they have been witnessing are because Fortinbras is marching on Denmark with an army to avenge his father's death. Horatio says he will tell Hamlet about the ghost.
We then learn that Hamlet, son of the late king, is upset that his mother married Claudius so quickly after the death of her husband. Hamlet expresses in a soliloquy his sense that Claudius is not half the man his father was and conveys his deep distress that his mother married Claudius. Hamlet also communications his depression and desire to kill himself.
We are introduced to Polonius, his son, Laertes, and his daughter, Ophelia. Polonius is an important advisor to Claudius. Polonius gives Laertes much advice as he heads off to France, and he sends a spy to keep an eye on Laertes. Laertes advises Ophelia not to get too involved with Hamlet, as he is a prince and his marriage is an affair of state. Hamlet will love her and leave her, Laertes says.
Hamlet goes to the rampart. The ghost speaks to him as it has not to the others and tells him that it is his late father. The ghost also informs Hamlet that Claudius murdered him and demands that Hamlet avenge his death.