Is Shakespeare's Hamlet character mad?

Shakespeare has a way of writing creating his characters for each play he wrote; each have their own individual faults and issues that we learn about throughout the plays. Hamlet, being one of the more famous of Shakespeare's creations, has his issues with his mother, deceased father and his new father, or rather his uncle. Throughout the play we hear of a ghost appearing to the watchmen, it appears only briefly each night and wearing …

…over his emotions and actions through the play, he cares not for his own life, such as when he follows the ghost, even when it may be a demon who can slay him and drag him to the depths of hell. Hamlets state of mind is perpetually in the darkness, he never has a happy moment through the play, at no point does he express a great happiness without his melancholy emotions still on show.