What is the Climax in the play Hamlet?
Plays operate quite differently from novels. First of all, they aren't written to be read by an audience at all, but witnessed live as a complete performance, of which the script (the written text) is only part of the equation. Actors bring action and life to the words written on the page by the playwright. So, a play-script itself, as a work, can definitely be considered incomplete when simply read. This, as you might gather, is exactly the opposite of a novel which is written by the novelist with the intention that it be read by one person.
The play Hamlet, structurally speaking, is quite debated over in terms of rising and falling action. The climax of a work of drama, would be the moment of greatest intensity, the moment in which the audience is most on the edge of their seats, wondering what will happen next.
One point of view on the play would suggest that this moment comes in Act III, scenes ii and iii, when (in scene ii) Hamlet discovers, through the play within a play, The Mousetrap, that Claudius must be guilty of murdering Hamlet's father (based upon his reaction to the play). In scene iii, he finds Claudius on his knees and comes within a hair's breath of killing him. But he does not. Hamlet lets Claudius live, and this action could been seen as the beginning of the denouement of the play, as all the action that follows drops in intensity from this missed opportunity for revenge. Hamlet is shipped off to England and drops out of the events for a few scenes, signalling an end to an important sequence of events, thus marking the climax of the play.
On the other hand, another possible climax of the play occurs in Act V during the duel. The audience knows that Claudius and Laertes are plotting to use the duel as a means to murder Hamlet. From this point, the audience is waiting to see what will happen. Will Hamlet be killed? This is a new sequence of events, of rising action, events arising from Claudius' and Laertes plot. The events in Act V build up to the duel, and the climax comes when Hamlet realizes that he has been poisoned and he actually, finally, murders Claudius.
Waht is the reason that there might be some confusion about the climatic moment in Hamlet? We have different versions of the script, with scenes added, missing, in different order, depending upon which Quarto or Folio you refer to. Because of this, we have no "clean" script with a definitive structure that we can analyze. Again, Shakespeare wrote his text for his actors to speak onstage, not for a reading public, so the publishing of each play has presented complications when we attempt to analyze them as works of literature.