How does Shakespeare explore the issue of revenge in "Hamlet"?
"Hamlet" actually owes a lot to the genre "revenge tragedy", very popular at the time Shakespeare was writing (have a look at, for example, Thomas Kyd's "The Spanish Tragedy" for an example of revenge tragedy that Shakespeare would have seen or read).
In revenge tragedies, more often than not, sons have to revenge their fathers, usually involving some sort of theatre, madness, or disguise ("Hamlet" has all three!) and at the end, vengeance completed, everyone dies.
Shakespeare even quotes from a well known revenge tragedy in "Hamlet", a play called "The True Tragedy of Richard III", which features the line which Hamlet speaks in the play scene: "Come, the croaking raven doth bellow for revenge".
The play is full of sons revenging their father: Hamlet (kills Claudius for killing Old Hamlet), Laertes (kills Hamlet for killing Polonius) and Fortinbras (invades Denmark to revenge his dead father, Old Fortinbras).
Yet Shakespeare, by employing various complicating factors - Hamlet's delay, the problem of religion and damnation, the theatrical nature of Elsinore, where no-one is what they seem - draws attention to revenge as a problematic obligation. Should you revenge? Is it right to revenge? How do you revenge?
There's lots and lots to look at - start with Hamlet's soliloquy "O what a rogue and peasant slave am I" - and, of course, talking a little about revenge tragedy will get you extra credit!