Another week, another London theatre refurbished and reopened thanks to the loot from the Lottery and elsewhere, which has enabled and encouraged a vast range of playhouses to call in either the builders or a new artistic director. In this case, it is Michael Attenborough as the resident director, who has called in Trevor Nunn, until recently in charge of the National, to stage The Lady From the Sea. This production makes the best of the Almeida's original home; thankfully, the major changes only amount to more comfortable seating and an indoor foyer and bar.
Written in 1888 when Ibsen was living in Munich and clearly nostalgic for the fjords of Norway's west coast, The Lady From the Sea has always been a tricky one for actors and critics alike, since the entire drama hangs on one single decision made in the last act: I won't give it away, but ask you to recall the airport scene in Casablanca.
Over here, there has been only one major revival in the postwar years, back in 1979, when the central role of Ellida was played by Vanessa Redgrave. A quarter-century later we get her daughter, Natasha Richardson, unmistakably a Redgrave from the tall, gangling stage presence to a voice that sounds like gravel run through honey.
However, for the play to work, and it was a triumph for Eleanor Duse a century or so ago, you need an extraordinary actress capable of suggesting a whole other life: but they don't teach how to be mesmeric at drama schools - even to Redgraves. Ibsen pasted together a rather ramshackle plot to allow for a crucial debate about feminism, the rights of a wife within a marriage, and reasons for marriage itself. Written barely two years before Ibsen's best-known play, we can now see Ellida as a prototype for Hedda Gabler. Pam Gems's new version of The Lady From the Sea underlines its feminism but still doesn't really fix the problems of somebody who belongs to the sea rather than the land: the result is neither wet nor dry, just a little damp.
David Mamet found in his native Chicago a quick-fire dialect of the streets that had never before been used on stage. What he pioneered back in 1971, when he was barely 23, was a colloquial language that was still very new to the theatre. A Mamet speech can run for fewer than five words, at least one of them violent, crude or blasphemous; sometimes he manages all three. Hearing his dialogue and watching his characters in action is like finding yourself at the wrong end of a machine-gun.
There is a raw, naked energy in Mamet that takes us back to Clifford Odets and the grainy Warner black-and-white world of 1930s crime movies, but the cast, which includes Matthew Perry from Friends, Minnie Driver from Good Will Hunting, the triple Emmy-winning Hank Azaria and our own Kelly Reilly, fails to solve Sexual Perversity in Chicago's problems. Mamet was experimenting with various forms of dialogue and drama, and there is little time to care about his people. They exist in an emotional void; Mamet's men and women are always hoping for a better destination and always unable to escape the reality of their lives. So what we get in Lindsay Posner's inevitably static production are dry runs for later, more fulfilled work such as American Buffalo and Speed-the-Plow. What Mamet wants us to know is that we connect or we die: but no character gets rebuilt here, we just see them and then we don't. Mamet chronicles four of them as they crash into each other: nobody really knows where to go next. Nowadays, they'd make it over as a sitcom on cable television: but why not go and see the original.
0f all Shakespeare's histories, Henry V is most often staged in times of hostility: I have seen at least three set in the First World War; while the Laurence Olivier film became almost a recruiting poster for Britain during the Second World War.
So it was good of Saddam Hussein to give the new National Theatre director Nicholas Hytner the chance to stage a modern-dress version, with Adrian Lester in the title role, soundbites, video and all the machinery of contemporary battles. This is the CNN version of Henry V. Hytner takes each scene and charges several thousand volts at it, so we end up with tanks, armoured cars and a very expensive set. But Henry V is about more than war: it's about age-old treaties gone wrong; about the sanctity of the crown, and perhaps, most surprisingly, about love thriving across the Channel, as Henry decides to woo the French princess at the last.
Shakespeare simply wasn't writing about Iraq, however tempting it might be to imagine what would have happened if he had done so.
The Lady From the Sea is at the Almeida, London N1 (020 7359 4404) until 28 June
Sexual Perversity in Chicago is at the Comedy Theatre, London SW1 (020 7369 1731) until 2 August
Henry V is at the Olivier, National Theatre, London SE1 (020 7452 3000) until 20 August