Akram Khan, Purcell Room, London<br></br>Random Dance Company, Lilian Baylis Theatre, London

An audience with the rhythm king

Kathak – the classical dance of northern India and Pakistan – is no stranger to British stages, but it has taken the extraordinary input of a 28-year-old Londoner to bring kathak to a wider public, and this, curiously enough, through his work in contemporary dance. For Akram Khan is that rare breed of artist, equally at home in classical or avant-garde. One minute he's touring the globe with Kaash – his modish collaboration with artist Anish Kapoor and composer Nitin Sawhney – the next he's polishing classical steps with his guru. The cutting edge gains traceable roots; traditional gets a dose of glamour.

Last week saw Khan back in classical harness in a programme devised to mark the end of his tenure as the South Bank's choreographer-in-residence and launch him as associate artist – clearly, now they've got him they're not letting go. If on paper the evening looked recherché, the event proved once and for all kathak's thrilling accessibility. While it helps to know a smidgen of Hindu mythology, the virtuosity and sheer luminous beauty of Khan's performance give it a life far beyond the academic.

Tuesday's special performance could have been titled "Akram and Friends" with its eclectic contributions from writer Hanif Kureishi and White Teeth's Christopher Simpson alongside female kathak stars. But the highlight was Khan's new piece Ronin, the second of his trilogy of kathak solos, and no number of side-shows could dilute its intensity.

The name kathak originates from the word for story, and the narrative element remains strong. In Ronin, Khan and his co-choreographer Gauri Sharma Tripathi explore the dilemma of the great warrior Arjuna – a character from the epic Mahabharata and a reluctant fighter, despite powers of marksmanship allowing him to hit the eye of a revolving fish. And Khan's 30-minute solo dance remarkably conveys not only a vivid idea of Arjuna's power and precision, but also his tortured dialogue with the god Krishna, who eventually persuades him into battle.

As a classical dancer, Khan has the advantage of a warrior physique – his compact form and beautifully neat head and features fresh out of a moghul painting. But more than this physical harmony, it's his quicksilver moods that make him so transfixing. One moment he's all gentle grace, the perfect host offering home-made sweets or the artisan threading a loom; two seconds later he's like a crazed warlord. At its climax the work reaches an almost unbearable pitch. Khan's lower body vibrates with tension – an effect made audible by some 200 tiny ankle bells – while his torso and face assume a terrified stillness, as if Arjuna is peering into the pit of his own death.

Later in the evening, keen to deflect the limelight onto his four superb musicians, Khan relaxes into masterclass mode. Like jazz improvisers, Khan reeled off vocalised rhythms to his tabla player, Partha Sarathi Mukherjee, who duly returned the patterns, only to have them volley back again from Khan in a rattle of exquisitely inflected footwork. The exercise was meant to be instructive, but personally I'm no closer to fathoming the level of skill in this metrical wizardry.

What a pity the choreographer Wayne McGregor didn't take a more teacherly approach to his latest show, Alpha, possibly the first ever to pitch abstract contemporary dance to under-12s. On the face of it, McGregor is well placed to access kids' imaginations, not least in his obsession with computer imagery and robotics. But producing the hardware is one thing, and using it to usher children into the adult viewing experience quite another. In Alpha, "an enchanting tale for children" performed by McGregor's company Random, I fear he drastically over-estimates his audience. For one thing, kids love stories, and this isn't one. It does contain, briefly, a folk tale related by a computer-synthesised voice, but frustratingly it comes out as gobbledegook. Can eight to 11-year-olds relate to abstract modern dance without the help of a plot? From the glum response of my own child, I'd guess not.

Yet Alpha does contain some arresting images. McGregor's punchy, clubby, ballet-related style is punctuated with surprises. Chains of long low jetés flicker past so fast they scarcely seem human-generated. Two men flip a third above their heads and hold him horizontal in a wrist-grip. But these things excite because we know the normal limits. For 10-year-olds accustomed to the hi-jinks of Lara Croft, it's no big deal. The experience needs a human context, one that, paradoxically, McGregor works hard to deny.

Things are complicated further by a mesh front-screen and backdrop that carry projections before and behind the dancers. The dual effect is clever and some of the images are startling – a gold-veined ball that might be planet Earth or a human brain; a man's body whose skin peels back to reveal a mass of caviar – but others are simply baffling. More memorable are the dancers' inflatable costumes – shiny translucent butterfly wings, antlers, a jellyfish skirt. For a brief, happy time the dancers pretend to be these creatures. But a dance I'd decided was about two fireflies in the dark was meant to represent the dichotomy of man's relation to the natural world. Oh well.

j.gilbert@independent.co.uk

'Alpha': Theatre Royal Winchester (01962 840440), 29 & 30 April; and touring