Is Hamlet Mad?

Perhaps the world's most famous mental patient, Hamlet's sanity has been argued over by countless learned scholars for hundreds of years. As a mere student of advanced-level English Literature, I doubt I can add anything new to the debate in 2000 words, but I can look at the evidence supporting or dispelling each argument and come to my own conclusion.
Hamlet is obviously experiencing grief and despair right from the beginning of the novel, with the death of his father and his uncle's seizure of the throne and rapid weddign of Hamlet's mother, and we can observe his great grief bordering…