Explain the revenge aspect of the play between Laertes/Hamlet and Fortinbras/Hamlet.
Certainly, the young and tender Fortinbras is a great foil to Hamlet as he is a man who acts, rather than procrastinates. For, just as Prince Hamlet has vowed to avenge his father, so, too, does Fortinbras wish to reclaim Denmark for the kingdom of Norway. His willingness to risk his life for the sake of honor--
Exposing what is mortal and unsure
To all that fortune, death, and danger date,
Even for an eggshell-- (4.4.51-53)
inspires Hamlet, who has greater cause to avenge King Hamlet than his rival for the kingdom.
After Laertes learns that his father Polonius is dead, he seeks revenge against the murderer, whom he believes is King Claudius. However, when he bursts in upon the king, Laertes is told by King Claudius that his friend Hamlet is responsible. Further, Claudius convinces Laertes to conspire with him in the destruction of Hamlet. Claudius, then, asks Laertes what he would do to prove himself his "father's son," and Laertes replies, "To cut his throat i'th'church" ((4.7.124). To add to Laertes hatred of Hamlet, he learns that his sister has committed suicide partly because of Hamlet's rejection of her. He and Hamlet fight at her gravesite.
Claudius plans to have the rapier of Laertes dipped in poison, as well as a cup for Hamlet to drink if it appears that he is winning the duel. Of course, as the duel ensues, things do not go as planned and Laertes regrets his actions, apologizing to his old friend before dying.