Identify three instances of revenge in Hamlet, and describe them. Who is seeking revenge in each instance? What is the outcome in each incident?
One instance of revenge is with Fortinbras. He wants revenge because his father lost a fight to King Hamlet and thus lost his territories (Act. 1, sc. 2). Fortinbras puts together a group of mercenaries to achieve his goal. By the end of the play, Act 5, sc. 2, Fortinbras has successfully invaded Denmark and claimed the throne. He has achieved his goal of getting revenge. The loser is Denmark in that a Dane no longer sits on the throne of that country. Another instance of revenge is with Laertes. He wants vengeance for his father's death. Hamlet killed Polonius when Polonius was hiding behind the arras in Gertrude's chamber when Hamlet confronted her after the play (Act 3, sc. 4). In Act 4, sc. 7, Laertes and Claudius plot to have Laertes kill Hamlet when the two of them engage in a "friendly" duel. In Act 5, sc. 2, during that duel, Laertes does scratch Hamlet with his sword, the blade of which he has annointed with poison. During this scene, Gertrude falls having drunk from the cup of poisoned wine that was intended for Hamlet and then Laertes, realizing that Claudius was behind everything, tells Hamlet the truth. Hamlet does die, but not before Laertes, so Laertes never does get his revenge against Hamlet. Since Hamlet kills Claudius, both Hamlet and Laertes do get revenge against him for all the treacheries he committed including killing Hamlet's father, King Hamlet. Nearly everyone loses and dies here.
Another instance of revenge in the play is when Hamlet seeks revenge on his former friends, Rosencrantz and Guildenstern. If you will recall, King Claudius first asks them to come to Elsinore so that they can keep an eye on Hamlet and then report back to him (though he frames it in terms of them helping their friend, not that they would be spying on him). Hamlet figures this out pretty quickly and gets very angry with them for their attempt to deceive him about why they came, though they are relatively innocent and do not realize how they are being used by the king.
Then, when Claudius sends Hamlet, with Rosencrantz and Guildenstern, to England, Hamlet opens the letter Claudius wrote, which allows him to discover that Claudius has asked the king of England to kill Hamlet. Hamlet assumes that his former friends know about this plan, since he already distrusts them because they tried to lie to them about why they came to Denmark in the first place, and so he rewrites the letter, asking the English king to instead kill Rosencrantz and Guildenstern. When the ship engages with some pirates, Hamlet ends up on the pirate ship, which returns him to Denmark, while his old friends continue to their doom in England.
First of all, Hamlet is seeking revenge for his father's murder by Claudius. He spends the entire play wavering between action and inaction. He does get revenge, but it is at the price of his life and that of his mother and Ophelia. Laertes, in a parallel revenge, seeks revenge against Hamlet for killing his father, Polonius, and the untimely death of his sister, Ophelia. And like Hamlet, does get revenge, but it is also at the price of his life. Young Fortinbras seeks revenge, politically, against Denmark for the defeat of his father and against the Danish crown; he remains standing at the end of the play, so he could be called a victor. Claudius seeks revenge upon Hamlet for being a problem to his throne and his marriage; Claudius is killed in his attempt. There you have the revenge motif, briefly!