Act I: Guards on duty discuss seeing the Ghost of Hamlet's late father, the dead King, and then see him again. Hamlet's mother, Gertrude, has remarried to Hamlet's uncle Claudius, putting the King's murderer on the throne. The courtier Polonius pre pares his son Laertes for a journey to Paris. He then orders his daughter to stay away from Hamlet, her love, because he fears Hamlet is going mad. The Ghost appears to Hamlet and tells him he wants revenge on Claudius.
Act II: After a time lapse, Hamlet feigns madness, but cannot as easily fool Claudius as he does others. The two both want to kill each other, but both need a reason to justify it. The attacking Fortinbras is reported to have called off his strike on Denmark, but that remains to be seen. Polonius and Claudius try to trick Hamlet, but he stays ahead of them. Hamlet meets his old friends, Rosencrantz and Guildenstern, and is at first delighted to see them. But, he immediately realizes they are there to spy on him. Hamlet devises to use a play which show's Claudius's crime to prove him guilty.
Act III: Hamlet contemplates suicide, but Claudius is still not fooled and decides to send Hamlet to England, most likely to kill him. The play is done, and Claudius knows he must act or he will fall. Foolish Plonius asks Gertrude to question Hamle t. While the two are talking, Hamlet begins to grow angry at his mother, but the Ghost reappears and tells Hamlet to remember who it is that he is after. Inadvertently, Hamlet kills Polonius who was listening in from behind the curtain.
Act IV: Laertes is angry at Claudius because he thinks he killed his father, but the king consoles him. Claudius hatches a plan to kill Hamlet, who is back in Denmark because he escaped death in England via some wit and some pirates.
Act V: Hamlet finds out from a gravedigger that Ophelia is dead, and upon seeing her funeral, announces his love for her. Laertes challenges him to a match, but they do not fight just yet. They go back to the castle for a jousting match where...the Queen drinks a poisoned glass meant for Hamlet, Laertes wounds Hamlet, Hamlet kills Laertes, Laertes announces Claudius's evil intentions, Hamlet kills Claudius, and then Hamlet dies because Laertes was fighting with a poisoned sword. Before his death, H amlet tells Horatio to give authority to the approaching Fortinbras.
The summary of this play was taken from http://www.ocf.berkeley.edu/~anthony/Shake2.html