In Shakespeare's Hamlet, there are many references to revenge, for this is a revenge play, a form of drama particularly popular during Shakespeare's time.
This kind of play includes the murder of someone important—generally by someone evil; the ghost of the murdered person walking and speaking to a "younger kinsman;" subterfuge existing between the murderer and the avenger; the presence of madness or pretended insanity; the play closes amid extensive violence; and, devastation is visited upon the main characters in the drama.
This is a perfect description of Hamlet.
The first reference to revenge is found in Act One. Hamlet speaks to the ghost of his dead father, who charges his son to avenge his murder at the hands of Claudius:
If thou didst ever thy dear father love—
… Revenge his foul and most unnatural murder. (I.v.27, 29)
Young Fortinbras of Norway is (as the play begins) attacking Denmark because he (erroneously) believes his father was killed—and land taken—dishonorably. The inference is that Fortinbras is determined to avenge his father's death. He...
...Hath in the skirts of Norway here and there,
Shark'd up a list of lawless resolutes,
For food and diet to some enterprise
That hath a stomach in't; which is no other—
As it doth well appear unto our state—
But to recover of us, by strong hand
And terms compulsatory, those foresaid lands
So by his father lost. (I.i.110, 112-118)
Only when ordered by his uncle, now the King of Norway, does Fortinbras stop—for the terms of the battle were negotiated beforehand. Fortinbras acts immediately; Hamlet hesitates.
In Act IV, scene four, Hamlet passes Fortinbras' army—ready to sacrifice all for a small plot of land. Hamlet is amazed at the willingness of these men to die for so little. Hamlet has much more reason to fight, but still he has not killed Claudius. Starting now he will take action:
How stand I then,
That have a father kill'd, a mother stain'd,
Excitements of my reason and my blood,(60)
And let all sleep...
...O, from this time forth,
My thoughts be bloody, or be nothing worth! (58-61, 67-68)
In Act Four, scene seven, Laertes has returned to Elsinore. He blames Hamlet: he wants to avenge his father's death at Hamlet's hands, as well as his sister's mental deterioration. He tells Claudius:
And so have I a noble father lost;
A sister driven into desperate terms...
But my revenge will come. (27-28, 31)
We might assume that Hamlet wreaks revenge on Rosencrantz and Guildenstern as he arranges for them to be executed in his place. These two men are foolish and seem harmless, but they have turned their back on their friend for personal gain.
Finally, even as Laertes fights Hamlet intended to avenge both father and sister at the sword-fighting event, Claudius allows Gertrude to drink poisonous wine meant for him. By now Hamlet is ready to send Claudius to his death for his murder of Old Hamlet, so he avenges his father's death and his mother's recent demise:
Laertes informs Hamlet...
Thy mother's poison'd...
...The King, the King's to blame. (V.ii.327-328)
Again we hear Hamlet address himself to revenge as he kills Claudius:
Here, thou incestuous, murderous, damned Dane,
Drink off this potion!...
Follow my mother. (332-334)
This prevalent theme of revenge is found throughout the play. It drives Hamlet's actions, but his failure to act sooner costs the lives of everyone at court except Horatio.