This question can be approached from a variety of points, foremost of which is the psychoanalytical “Oedipus deferred” view, in which following the death of his father, the “Dane”, the villainous Claudius take the role of the father that must be destroyed.

Evidence of this can be obtained from Act one, Scene two, in which Hamlet the second has just learnt of his mother’s marriage, before his father’s ghost appears to deliver the metaphorical bombshell of his murder. This scene is interesting, as it provides a core piece of evidence: Even before he learns the truth, Hamlet is distrusting of Claudius for the “Unseemly speed” with which he moves in on Gertrude.

This much we can deduce from his soliloquy, in which he comments on how much the Dane loved his wife Gertrude, only for her to move on so rapidly to the pleasures of Claudius’ “Incestuous Sheets”, hinting at themes and ideas still to come in the play, and also revealing Hamlet’s low opinion of women, tarring them with the same brush as it were. These themes are vastly expanded in both the “Closet” and “Ophelia” scenes, which I will visit later.

Now, I shall move onto Act one Scenes four and five, in which Hamlet first meets and then speaks to the ghost of the Dane. This scene proves something I suspect we all knew, that teen angst is nigh-on universal, as we hear of Hamlet’s depression and suicidal tendencies, stating that he “Does not set (his) life at a pin’s fee”, and revealing a hint of the ennui which will eventually lead to the famous (or, from the perspective of the generations of children forced to study it, infamous) “To be or not to be” soliloquy, where he finally confronts the demons of his psyche and the self-destructive impulses they cause in him, and would put them down to move on with his quest, were it not for the interruption of Ophelia at an inopportune moment. In scene five, however, we see Hamlet’s reaction to the truth of his father’s murder, and witness what seems almost to be nothing more than a crystallisation of a prior objective: The death of Claudius, the “Smiling… Damned villain” of the piece. In this scene, however, there is almost no mention of his mother’s incest, and after the ghost’s piteous retelling of his plight, he decides to help avenge the Dane’s death. But, Hamlet still seems unconnected from the situation as he coolly and calmly plots the murder of his own uncle, in a masterpiece of the “Eye for an Eye” attitude so despised by Ghandi.

In Act two Scene Two, we find that Hamlet is still not entirely emotionally concerned with either of the two main issues, or rather that he cannot become emotionally attached to anything, to a degree where he almost envies the player who, over a simple script, could force his spirit … on conceit” and shed tears over the fictional Hecuba as, after all, “What’s Hecuba to him, or he to Hecuba?”

However, in this scene, he swings entirely from the wedding, focusing exclusively on the murder and casting aside all questions of propriety and incest to focus on tricking Claudius into admitting his guilt in the murder must foul. This leads me further into my thesis that, if not strictly Bi-Polar, Hamlet still has violent swings between vitriolic highs where he becomes aggressive and hateful to womankind in general, and Gertrude and the blameless Ophelia in particular, to depressive lows where he ponders the nature of life in general (and it’s end), much like the titular character in Kurosawa’s seminal work, “Roshambo”. Indeed, it is a strength of Shakespeare, that he may create characters with emotional complexity matched only by such infamous characters as Hannibal Lecter, whose motives may be peeled away for years and the true meaning still not found.

Further evidence for this theory may be found in the infamous Hallway scene, Act Three Scene One, where Hamlet violently shifts from pondering why he should continue living when “He himself might his quietus make”(End his life) “With a bare Bodkin” (An unsheathed knife), to a rant about the unfairness of the female species, their ungodliness, and the loss of virtue in the pursuit of as elusive a concept as beauty. (In which an interesting parallel may be drawn to today’s society in which their less talented but more “Attractive” compatriots may freely harass the intelligent. But I digress.) This scene is the metaphorical “Home Run” for those that believe his mother’s infidelity is what troubles him the most, as he finally shows some real signs of emotion when talking about the evils of women, as opposed to his slow ponderings on the great truths.

Next, we come to the closet scene, Act Three Scene Four.

In the beginning, we see that Hamlet isn’t paranoid, as they really all are out to get him.

The arras loving Polonius hiding behind a curtain, Hamlet confronts his mother, her presence finally seeming to spark an emotional reaction from him, the “Native hue of resolution” no longer “Sicklied o’er with the pale cast of thought”, he is finally galvanised into action and (We presume) throws her to the bed, in order that he may say his piece. This action, however, leads him to his first murder, that of (the deserving) Polonius.

We notice, however, that he no longer cares about the innocent life that he has snuffed out, only caring if it is the king or not. Hamlet does appear relieved, however, when it is revealed that his mother knows nothing of the murder. Now, however, he becomes incredibly vitriolic about the difference between Claudius and the Dane, showing how deeply he cares about the marriage, and has to be verbally restrained by the ghost before he becomes so vicious as to destroy all hope of redeeming his mother.

Upon seeing the ghost, he is seized with guilt, as he realises that he has delayed his task of revenge to chastise his errant parent. Here, we sense that he and the ghost may have a slightly different agenda, and so Hamlet’s priorities are finally thrown into sharp relief: Mother first, Murder second.