Even the purists might be satisfied by this version of Euripides' great 5th century BC play, the second in the Almeida's trilogy of the Greeks, and a production by James Macdonald that is close to the original in its text (a springy, witty version by Canadian poet Anne Carson, who translated Sophocles' Antigone for Juliette Binoche and Ivo van Hove) and yet absolutely pertinent for our times.

There is a chorus of female Bakkhai, travelling good-time groupies, but singularly identified as women, too, who've assembled on the Theban mountain to follow Ben Whishaw as Dionysus, aka Bacchus, god of wine and ecstasy, who's disguised himself as a man; in the prologue, he stands before us in messianic long hair and a white T-shirt to explain the back story and his own divine genealogy (son of Zeus, basically, with complications).

Trouble is, the king of Thebes, Pentheus (Bertie Carvel in a sleek suit with a giveaway streak of white face paint on his nose), has banned the gigs and rituals as decadent and hedonistic, incompatible with decent behaviour; but, like Lord Sewel the other day, he's soon hoist on own petard.

And then there is a third fine actor, Kevin Harvey, as the old king Kadmos, doubled with a servant, and teaming with blind prophet Tiresias (Whishaw again) to warn Pentheus of his censorious folly before rushing off to join the party.

The chorus – who include Helen Hobson, Kaisa Hammerlund, Belinda Sykes and Catherine May – sing, brilliantly, and a capello, some extraordinary and subtly coloured harmonic settings by Orlando Gough of the descriptive and critical speeches, clad in their regulation outfits of fawn skins, ivy laurel wreaths and thyrsos (stomping sticks of gnarled wood).

This form of chorus and three actors – Carvel is poignantly doubled with his own mother, Agave (and she's nothing to do with Miss Trunchbull; well, not too much) – exactly follows the Greek model. And you see the point of it as the play is about transformation, moving through one's own mythologies, not just a face-off between the polar opposites of man and god, sex and sterility, sanity and madness.

In rediscovering the form, Macdonald releases the ambiguities and complications. These are best expressed in the scene where Carvel's faintly magnetised king sets out to interrogate Whishaw's taunting rock star Dionysus (Ben will have to iron out these subtleties when he gets going on Freddie Mercury in a forthcoming movie) only to find himself dragged in, and, before you can say Mount Cithaeron, dragged up.

The uninterrupted two hours flashes by without once veering towards the domestic banality or soap opera excesses of the Oresteia last month. The impact and poetry of the tragedy is all the more powerful for being rooted in its origins; it's certainly one of the best Greek tragedy – as opposed to geek tragedy - productions I've seen for years. And I'd recommend it to anyone who wants to know what all the fuss is about with those old plays, let alone why Euripides is among the greatest dramatists who ever lived.

Bakkhai runs at the Almeida until 19 September. Click here for more information and to book tickets.