"The play doesn't have a single arc like Macbeth, Othello, or even Lear. It's about so many things - family relationships, love and jealousy, public and private faces, theatricality and performance, life and death and the nature of life after death."
Despite its complexity, the play is more accessible than any of the tragedies, says Alexander.
"Few of us will become serial murderers, or marry an Egyptian queen, but we all experience the tensions of family life. We are familiar with feelings of rejection, of jealousy, and the turbulence of love."
This domestic element will be strengthened by Alexander's decision, in creating his own conflation of the Second Quarto and First Folio texts, to cut out "Fortinbras and the whole Norway thing". Claudius will not send ambassadors to the Norwegian king, Hamlet will not meet the army Captain on the shore and meditate on "How all occasions do inform against me", and Fortinbras will not take over the Danish court. The tensions will be domestic, not political.
Similarly, in exploring Hamlet's character, Alexander and his leading actor, Richard McCabe, steer away from the wilder shores of psychology.
"There is no suggestion of incest or real madness", says Alexander. "Hamlet does what he says he will do. He feigns madness as a way of getting to the truth. Of course his emotions are running high, and feigned madness is a way of giving vent to them."
The mix of careful thought and impulsive action makes for a sense of danger, a quality Alexander prizes in McCabe's acting, "But he is also very witty, and Richard is good at being dangerous and funny," he says.
And Hamlet's fatal flaw? "That's not easy to discover," says Alexander. "I don't see it as prevarication. Hamlet hesitates no more than the rest of us would in the face of what he's been asked to do, but he takes rejection badly. His mother's unexpected marriage displaces him from becoming the man of the family and Ophelia's sudden apparent rejection of him brings an immediate response of aggression."
How many vulnerable teenagers in the audience will find this quality in the Prince, and, as Alexander suggests, feel the play "touching their lives more closely".
'Hamlet' runs at Birmingham Rep from tonight until October 10. Box office: (0121) 236 4455. Education enquiries to Rachel Gartside: (0121) 236 6771.