“Jazz is my adventure,” said Thelonious Monk. “I’m after new chords, new ways of syncopating, new figures, new runs. How to use notes differently. That’s it. Just using notes differently.” Based on the title of the new hour-long piece by Israeli choreographer Emanuel Gat, Brilliant Corners, named for Monk’s 1957 album, the naïve viewer might expect, at the very least, to hear some Monk. Not so. Gat has produced an always interesting, sometimes absorbing sight-and-sound world, but of Monk, or jazz, there is neither sight nor sound.

The cool physical activity of McGregor’s Limen, the crimson passions of Ashton’s Marguerite and Armand, the symbolic sculpture of MacMillan’s Requiem - the weekend's new triple bill at Covent Garden shows three faces of British ballet-making over the past half-century. While none is the masterpiece of its creator, together they describe an arc over time where lyrical emotion became replaced by gymnastic motion, compression by diffusion, individual idiosyncrasy by a kind of balletic collective.

Any newcomers to Merce Cunningham who visit the last performances ever in Britain of his modern dance company - renowned, even notorious, for its abstruse abstractness - will surely go away with an impression of laughter, playfulness, the lightness of being. On two more nights, tonight and tomorrow, this landmark company will perform his dances, and then - like the end of his piece Ocean, which you can see on film tomorrow - when the clock runs out, the last dancer will leave the stage, and that will be the end of it.

It takes more than utmost craft and rich personality to hold the stage as a soloist - it takes a touch of divine self-belief, which Akram Khan has never displayed to more magnetic effect before than in his new solo DESH. Actually solo is too small a word for this epic, lavish display of the starpower that Khan now emits in the world of dance theatre.

Dance is eating itself. Or dancers are eating themselves, rather. It's on-trend to defy the idea of the mute dancer, and instead have them verbally explaining themselves, their motivation, their art. This year’s Dance Umbrella launched last night with the “self-contemplation” of Cédric Andrieux, a handsome blond Frenchman, who regales us in a charming murmur for 80 minutes with the story of his career, with danced illustrations.

The first half-hour of Edouard Lock’s nameless new piece is some of the most thrilling dance imaginable; dynamic, mercurial, as men and women convulsed with frenzy fight each other in stark spotlights in the dark. They’re dressed in black, so that each flail, each clash, each twitch of a pink pointe shoe trails an outline of blinding light and throws a flashing black shadow. Mile-a-minute in the dark, it’s terrifying.

My acid test for whether a show’s worth going to is, specifically, whether it was worth driving 27 miles into town and 27 miles back, spending, say, three or sometimes four hours travelling to see something 80 minutes long. Not often is it worth that. But if it was on in a theatre near you, it would be worth picking up. And so I say for Arthur Pita’s The Metamorphosis.

On six more occasions you can have an ideal experience of dance by visiting the Degas exhibition at the Royal Academy and then going to see Balanchine’s Jewels at the Opera House.

Edit, edit. Inside TeZukA there’s a charming, elliptical, hugely stylish piece begging to be sliced and trimmed into focus - just as the manga master Osamu Tezuka must have daily occupied himself with as he prepared his graphic cartoons. The visuals in Sidi Larbi Cherkaoui’s piece are spectacular video animations of Tezuka’s fastidiously drawn scenes, the kerpows and the Zen landscapes, Black Jack, the transfigured rabbit. If it does nothing else, this show should whet your appetite for manga.

Shen Wei is only 43, but he’s packed an epic amount into his career. A child sent from home aged nine to study opera; an emigrant to New York; a return to China to choreograph the Beijing Olympics. His urge to put this extraordinary tale into dance theatre is understandable. That Re-Triptych, a semi-biographical creation that’s one of the Edinburgh International Festival’s features in its Asian dance programme this year, is only intermittently intriguing to watch, and largely inchoate in choreography, seems also understandable. Some experiences are just too much to render in art.