What happens in the rising action, climax, and resolution of the conflict in Hamlet?

In Hamlet, after Prince Hamlet has learned that his uncle killed his father in order to marry the Queen and become King, Hamlet is faced with a moral dilemma:  He does not know whether he can serve the cultural ritual of revenge, as urged by his father's Ghost, in this corrupt world without sacrificing his moral integrity ("To be or not to be").

In the rising action, Claudius and Gertrude seek the reason for Hamlet's "madness," and the King plans to send Hamlet to England.  Meanwhile, Hamlet exposes the King's guilt with a play, The Murder of Gonzago.  But, Hamlet delays killing Claudius whom he finds in the chapel supposedly at prayer. He drives his sword through Polonius who is hiding in Gertrude's chamber and who alarms Hamlet by crying out for guards.  Ophelia, Polonius's daughter, goes insane over the loss of Hamlet's love and Hamlet's murder of her father after Hamlet leaves for England where he is secretly to be assassinated; but the Prince rewrites the letters to have his betrayers killed instead. Ophelia dies; Laertes returns and throws himself upon her casket, asking to be buried with her while Hamlet, newly returned, discovers them in the cemetery and throws himself on her coffin, too.

The climax is in Act V, Scene ii. Claudius invites Hamlet to fence with Laertes. Hamlet accepts, saying "readiness is all" and asserting his belief in fate.  Gertrude drinks from a poisoned cup intended for Hamlet. Laertes wounds Hamlet. Hamlet and Laertes scuffle and rapiers are inadvertently swapped. With the poison-tipped foil Hamlet now holds, Laertes is stabbed. Dying Laertes tells him, "The king's to blame."  Hamlet turns the poisoned foil on Claudius and forces him to swallow the remaining drink of poison. 

In the resolution Hamlet, cut by the poisoned rapier and dying, drinks the dregs from the poisoned cup (though Horatio begs for it as he wants to die with his friend). He dies (reiterating the theme of death) after entrusting Horatio with telling the untold events and clearing his name and after endorsing Fortinbras as the next King of Denmark.

O good Horatio, what a wounded name,
Things standing thus unknown, shall live behind me!
If thou didst ever hold me in thy heart
Absent thee from felicity awhile,
And in this harsh world draw thy breath in pain,
To tell my story. (V.ii)