He wants the kingdom to know how Old Hamlet was murdered by the devious King Claudius and then they will know the truth and reasoning behind his madness. He tells Horatio "tell my story" (5,2,342) he wants everyone to know the truth.
Hamlet was a man of strong religious beliefs, he is constantly referring to god, "o god" (1,5,24), "god! o god!" (1,2,132). Hamlet is uncertain whether this ghost is truly his father's soul or an evil that has taken over his body, this concerns him if he takes revenge for his father what will happen to him will he go to hell? "O all you host of heaven! O earth! What else? And shall I couple hell?" 1,5,93). Hamlet also doesn't want Claudius to go to heaven he wants him to suffer like his father. In Act 3 Scene 3 Claudius is down on his knees struggling with his conscience and tries praying for forgiveness, Hamlet than enters seeing him on his knees and believes that he is praying. This would have been the perfect opportunity for Hamlet to act out his revenge, Claudius is all alone in a church, not suspecting anyone else to be around. Hamlet then begins to discuss how if he killed Claudius now he would surely go to heaven, after asking for forgiveness for his sins. This for hamlet would not be considered a good revenge, sure Claudius would be dead but he will not be suffering in his afterlife, Hamlet feels he needs to suffer for eternity "his soul may be damn'd black as hell, whereto it goes" (3,3,95). Hamlet decides he will wait until he has sinned again, "when he is drunk asleep, in his rage, or in the incestuous pleasure of his bed" (3,3,90). Hamlet knew he could not kill Claudius because of his beliefs, he knew that if God wanted Claudius dead, it would happen. He told Horatio "There's a divinity that shapes our ends, Rough-hew them how we will." (5,2,10-11). Hamlet feels that no matter how much we try to control our own lives it is already pre-determined by God.
