In Hamlet, there is an act of betrayal by Claudius. Then the entire play revolves around young Hamlet's desire to avenge his father's death:
Hamlet is often called an "Elizabethan revenge play", the theme of revenge against an evil usurper driving the plot forward.
Hamlet is a play that causes young Hamlet to not be able to rest until justice is served. Hamlet spends part of the play questioning whether or not his Uncle Claudius could do such a thing as murder his father. Once Hamlet is convinced that Claudius has indeed murdered his father, he spends the rest of the time plotting his retaliation for the murder of his father. The end result is a tragedy:
But Hamlet is far more than an outstanding example of the revenge play. It is, to begin, a tragedy in which the attainment of justice entails the avenging hero's death.
The theme or message is that revenge itself is deadly. Hamlet causes his own downfall by his obsession with revenge. By plotting Claudius' death, Hamlet is stirring up Claudius' natural reaction to protect himself. Ultimately, revenge kills Hamlet. His death is inevitable:
Life inevitably yields death and a wormy grave, and its occurrence cannot be foreseen or avoided.
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Hamlet is all about Revenge for his father, that's what the whole story is about!