Hamlet is a tragedy where revenge is an important part, but I don't think that Hamlet simply wants revenge. Hamlet's tragic flaw is not so much pride as sensitivity, in my opinion. He is not ready for the world he gets thrown into.
Hamlet is more a psychological play because the revenge is not enacted until the final scenes. Unlike most revenge plays, the action is postponed; so many feel that Hamlet is more about indecision and melancholy than it is revenge. For, so many questions are posed with this drama among them How can we know the certainties of a crime without witnesses? What knowledge can we know for certain? What real worth does the human life possess? Critic Harold Bloom, an authority on Shakespeare, contends that Shakespeare is our first psychologist with his play Hamlet.
I assume your question is whether Hamlet is a revenge tragedy. Of course, it is widely accepted as such, and Shakespeare makes direct reference to the tradition with the play within a play. Both that and Hamlet are updates of an Italian Picarro play called "The Murder of Gonzago." Revenge, of course, abounds in this play, with the three foils, Hamlet, Laertes, and Young Fortinbras all seeking revenge from those they perceive to have caused their fathers' deaths. The really interesting question Shakespeare asks is whether revenge is ever a valid action. Clearly each act of vengeance in this play results in supreme disaster. Even the victory of Fortinbras at the end comes at great cost to someone, and, interestingly, his celebration is tinged by sadness over the death of Hamlet. Is revenge ever justified? There seems to be a human desire to get revenge when we feel wronged, and we can find many instances in literature and specicically in Shakespeare of characters seeking vengeance, but clearly the author believes seeking revenge is a fool's mission. Good rarely comes of it and revenge damages and diminishes the perpetrator. After al, getting joy from the suffering of another is hardly a noble act. Hamlet is spurred to get revenge by both the external ("sometimes) ghost and his own feelings of anger, loss and jealousy. How did the whole revenge thing work out for him? That should give you a pretty good indicator of what revenge is truly worth.
Hamlet is considered a tragedy, and the character Hamlet himself is considered a tragic hero.
A tragedy is a story in which there is a tragic hero who is a generally 'good' or likable character, but who has a flaw. "A mole of defect". This flawed character commits a sin or a crime during the course of the play, and as a result of the characters flaw, or sin, the character must die. In the story, it is Hamlet’s inability to avenge the murder of his father that drives the plot forwards and the deaths, of Polonius, Laertes, Ophelia, Gertrude, Rosencrantz and Guildenstern all result from Hamlet’s delay.
To highlight Hamlet's inability to take action, Shakespeare includes a number of other characters capable of taking resolute and headstrong revenge as required. Fortinbras travels many miles to take his revenge and ultimately succeeds in conquering Denmark; Laertes plots to kill Hamlet to revenge the death of his father, Polonius.
What about it?