Edward Albee was 73 when The Goat, or Who Is Sylvia? first opened on Broadway in 2002 and the play makes me think of a late painting by Picasso or cut out by Matisse. It's a graceful tour de force, still full of challenge and dare and invention but executed with the precision of a master.

Part tragedy – what happens when a man with a perfect life is undone by a fatal flaw – and part ferocious social comedy – how far is society prepared to tolerate difference – it is both apparently simple and utterly complex. It also contains one of the single best dramatic jokes about the use of ‘who' and ‘whom' in the English language.

I think it is wonderful, invigorating and thrilling. Its premise is absolutely contained in that cryptic title; this is a story of a prize winning Manhattan architect called Martin, a man for whom the word uxorious might have been invented, who has never looked at anyone other than his wife Stevie in 22 years of marriage. But then he falls in love with Sylvia, a goat, and his entire life comes crashing down around him. Almost literally, as Stevie, in fury, destroys the trappings of their home, while their gay son Billy watches in horror.

The structure is, as you would expect from the man who won the Pulitzer Prize for drama three times, as sophisticated and exact as a Swiss watch. In the first act, there is revelation, when Martin is tempted to confess his ‘affair' to his best friend Ross, a film maker he has known since they were 10. The second act brings confrontation, when Ross feels obliged – "I am mortified to tell you" – to write Stevie a letter revealing all. The third, brings various kinds of resolution, most of them shocking.

Within that shape, the language shares the same delicate justness. Over and over again, Albee finds exactly the right word or phrase whether making jokes about Goat Fuckers Anonymous and a man who is screwing a pig – "a small one" –or dealing with the dangerous and morally ambivalent realms of how someone who is committing bestial acts can call his own son a "fucking faggot." The sheer density of the writing means that the play can be taken as being about many themes, and it does encompass all of them. But at its dark centre is a heartfelt examination of exactly what it takes to break a liberal, right-thinking family apart. Because Martin's problem isn't only his obsession with Sylvia; it is his belief he loves her. "I love you and I love her. There it is."

In Ian Rickson's carefully judged production, which on Rae Smith's imposing but slightly over-elaborate set travels from light to darkness both physically and metaphysically, it is Sophie Okonedo as Stevie who most perfectly catches the emotional tug that gives the play its impact. Her shock and righteous anger are beautifully but simply caught; she is funny but genuinely heart-breaking. She makes you believe and makes you care.

Damian Lewis's performance as Martin is more outward facing. It's full of clever detail like the way Martin's vagueness means he can never find a pocket in which to put his glasses, or the sense that he is caught unawares by his own emotion. He faces Stevie with a kind of defiance, his hands still at his sides, his head tilted as if bracing himself against her accusations. The conflict between them sometimes flows like a perfectly orchestrated aria but sometimes Lewis's prissy fastidiousness, the very eccentricity with which he endows Martin, seems to stand in their way.

The same hesitancy is also true of Archie Madekwe's Billy, the sad son who longs for love and attention amidst the wreckage, though I suspect both performances will relax as the run progresses. As Ross, the final player in this quartet, Jason Hughes captures just the right odious man about town air; he settles down to enjoy Martin's revelation about an affair, only to be shocked to his core not by the act, but by the fact that it might be discovered.

The revival of Who's Afraid of Virginia Woolf might seem a more obvious way of marking the genius of Edward Albee who died last year. But The Goat is a reminder of the way his genius did not fade; he could still nail the vagaries of the human soul right to the end.

The Goat, or Who Is Sylvia? is currently booking at Theatre Royal Haymarket until 24 June.

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