Hamlet wasn't mad - he was ambivalent
Freud thought that Hamlet had repressed his desire for his mother and that the circumstances of the play destabilized this represstion.

Harold Bloom in THE WESTER CANON says that
1. "Shakespeare was careful to show that Prince Hamlet was rather a neglected child, at least by his father. nowhere in the plahy does anhyone, including Hamlet and the Ghost, tell us that the uxurioius (greedy) father loved the son. ...the fractious king seems to have had no time for the child between the demans of state, war and husbandly lust. Thus, when the Ghost urges Hamlet to revene, it cries out "if thou didst every they dear father love,' but says nothing about its own affection for the prince. Similarly in his first soliloquoy exmphasies the devotion between his father and mother while excluding their regard, if any ofr him. His own memories of love, taken and given, centre entirely upon poor Yorick, his father's jester, who took the place of parents so smitted with one another."

2. Shakespeare so opens his characters to multiple perspectives that they become analytical instruments for judging you. If you are a moralist, Falstaff outrages you: if you are rancid, Rosaling exposes you; if you are dogmatic, Hamlet evades you forever

Hamet, the most fecund [of Shakespeare's characters with great wit, Falstaff, Rosalind and Hamlet] is endowed by Shakespeare with something that looks very much like an authorial consciousness and not not Shakespeare's own. Interpreting Hamlet becomeas as diffiult as interpreting such aphorists as Emerson, Nietsche and Kierkegard. I do not mean that Hamlet is Shakespeare. Hamlet is a miracle of inwardness.

At every moment, Hamlet's mind is a play within the play, because it is Hamlet, more than [any other character] in Shakespeare who is the free artist of himself. his exaltation and his torment alike stem from his continuous meditation upon his own image. The introspective consciousness, (Hamlet) free to contemplate itself, remains the most elitist of all Western images...

Iago and Edmund and Hamlet contemplate themselves objectively in inages wrought by their own intelligences and are enabled to see themselves as dramatic characters...They thus become free artists of themselves, which means that they are free to write themslves, to will changes in the self. Overhearing their own speaches and pondering those expressions, they change and go on to contemplate an otherness in the self, or the possibility of such otherness.