Denmark is under threat of invasion from young Fortinbras, who seeks to regain lands lost to Hamlet’s father by Fortinbras’s father.
Claudius sends word to the King of Norway (Fortinbras’s uncle) to curb Fortinbras’s aggression.
They employ a pair of Hamlet’s friends, Rosencrantz and Guildenstern, to watch him.
When Polonius, the pompous Lord Chamberlain, suggests that Hamlet may be mad with love for his daughter, Ophelia, Claudius agrees to spy on Hamlet in conversation with the girl.
When Horatio and the watchmen bring Prince Hamlet, the son of Gertrude and the dead king, to see the ghost, it speaks to him, declaring ominously that it is indeed his father’s spirit, and that he was murdered by none other than Claudius.
Moreover, Hamlet struggles with his doubts about whether he can trust the ghost and whether killing Claudius is the appropriate thing to do.
And if he--not his friend, not his mother, not his pastor--sees a ghost, he will acknowledge as such.
That's why Horatio freely admitted upon seeing the evidence. Revenge, ambition, lust and conspiracy return to the heads of those that conjured them in Hamlet, completely annihilating two families--the innocent with the guilty.
Polonius believes Hamlet’s “madness” to be love sickness.
Laertes is given permission to return to his studies in Paris.
We do know that Ophelia is torn between two contradictory poles.