"Notes on Hamlet"

Things are always changing and happening in the play making me keep making educated guesses on what is going to happen next. I understood what is happening in the play right now. How Hamlet had a play within a play to see if Claudius really killed his father. Then when Hamlet is about to kill Claudius he doesn't because he want him to suffer an agonizing death. He doesn't kill him out of respect, the real reason why he doesn't kill him is because he want him to be in more pain and wants to make sure when he kills him he going "straight to hell". I see Hamlet coming and killing Claudius  and then reclaiming his throne and becoming king.