In "Hamlet" does Hamlet think he is mad himself?I know some characters think that Hamlet is mad but I'm not sure if Hamlet thinks the same as those other characters.
I don't believe that he thinks he is mad. In fact, he confesses after the ghost appears that he is going to put on an "antic disposition" in order to throw people off. That antic disposition is the kooky, distancing, and alarming things that he does and says to make everyone think that he is mad. So, other characters feeling that he has lost his marbles is an indication that Hamlet's plan is working. He wants people to feel he isn't all there; that way, they won't take him seriously, and if he does something to alert Claudius that he's snooping around about the murder, Claudius is more likely to dismiss it, because it's just that crazy Hamlet being crazy again.
The only true glimpses that we get of Hamlet and what he feels about himself are during his soliloquys. In these, he ponders the meaning of life, and why we are such cowards about dying, he raves against his own cowardice in action-he says that all he does is "unpack his heart with words" instead of actually committing revenge. All of the thoughts that he expresses during these alone moments are completely lucid, logical, well-thought out, and don't deal with madness or insanity at all. If he was afraid of madness, when alone, he would express that fear; instead, he is afraid he is a coward, and that is his main concern when alone. So, madness is not something that worries him.
Those are just my thoughts; hopefully they can get you started. Good luck!