It's a collection of short pieces, some brilliantly illuminating (on the subject of mourning conventions, for instance), some quite silly. Carl Schmitt, Walter Benjamin, Hegel, Freud, Lacan and - yes - Nietzsche are all roped in, but it strikes me that while a psychoanalytical or philosophical approach to the play certainly enriches our knowledge, it may not add to our understanding.
In a Guardian article about their book the authors say, rather weirdly "The banal, biscuit-box Shakespeare needs to be broken up and his work made dangerous again."
'Biscuit-box Shakeapeare'? No, me neither. There's a glaring typo on the first page which augers ill ("I say there shall be no mo [sic] marriage"), the prose is uneven and there are rather too many threadbare hipster colloquialisms - has Hamlet really 'lost his mojo'? I mention this because I hope the authors would be equally impatient if I blundered into their respective fields and wrote things like "Wittgenstein was a well brainy dude" or "Freud had a thing about sex". Tone, see?
A more pervasive weakness is that the authors settle on and adhere to one entirely conventional interpretation of both Hamlet and Hamlet (although one that only gained currency in the early 20th century), namely that the Prince is banjax'd by indecision and that it is his failure to act that leads to his tragic downfall.
Yet by the final curtain Elsinore is a necropolis, proof that Hamlet is certainly capable of decisive action - ask Polonius.
Gertrude poisoned, his usurping uncle Claudius both stabbed and poisoned, while Laertes and Hamlet himself are both stabbed with the same poisoned rapier. Practically everyone dies apart from Horatio and Fortinbras. Of course if Hamlet acted immediately on hearing from the ghost of his father that he should avenge murder most foul, the play would be over in ten minutes. Then where would we be?
The Hamlet Doctrine is full of good things, although nothing as memorable as these lines from Tom Stoppard's Rosencrantz and Guildenstern are Dead in which Rosencrantz (or possibly Guildenstern) consider how best to question the Prince:
"To sum up: your father, whom you love, dies, you are his heir, you come back to find that hardly was the corpse cold before his young brother popped onto his throne and into his sheets, thereby offending both legal and natural practice. Now why exactly are you behaving in this extraordinary manner?"