In the doldrums for far too long, the Bolshoi is on the way to reclaim its position as one of the world's leading companies

In recent years, the Bolshoi has been eclipsed by the Kirov. While the Kirov flourished post-perestroika, the Moscow theatre and its management were in disarray. The ballet company was booked into dubious venues - Las Vegas, the Royal Albert Hall - by dodgy impresarios; tours by troupes styling themselves Stars of the Bolshoi proved to be anything but.

Now the company is fighting back. For this three-week season, it's at the Royal Opera House, presented by the Hochhausers, who last brought them to the London Coliseum in 1999. The repertoire is a mix of old and new, reflecting the policy of the company's latest artistic director, Alexei Ratmansky.

He's the fourth director since the ousting of Yuri Grigorovich, set in his autocratic ways after 30 years at the helm. Whether Ratmansky can successfully juggle 19th-century classics, Soviet epics and newly commissioned works, including his own choreography, has yet to be determined.

He chose to open the season with an old warhorse, Don Quixote, performed a thousand times in the Bolshoi theatre since its creation there in 1869. The Moscow premiere was in the dead of winter and it's easy to see how the ballet's evocation of sun-baked Spain served as a fantasy tourist brochure for generations of snowbound Russians.

Soviet productions made changes to Petipa's original version over the years: the current staging by Alexei Fadeyechev clears away many accretions, reverting more or less to Alexander Gorsky's account at the start of the last century.

The painted backcloths are old-fashioned, the costumes freshly made, the lighting so bright that the audience applauded with delight at being able to see the dancers properly (though a first-night glitch left the stage in darkness soon after the start; ah, the joys of state-of-the-art technology). Don Quixote is packed with opportunities for the kinds of dancing the Bolshoi does best: virtuoso leaps and lifts, soulful backbends, characterful carousing. The ballet operates like a firework display, each solo and duet more dazzling than the last, until everyone erupts into the grand finale.

Cervantes's novel is a mere pretext for the plot. The crazed Don, with Sancho Panza as his minder, helps unite bolshy Kitri with her impoverished lover, Basil. In the middle act, Don Quixote, knocked senseless by the sails of a windmill, has a vision of Kitri as his Dulcinea, surrounded by dryads in delicious tutus. That's it, apart from toreadors, gypsies and taverna table-dancers who provide exotic numbers to Minkus's jolly tunes - impossible to erase once they've infiltrated your memory.

The two casts I saw pointed up the contrast between new and old styles. Maria Alexandrova, recently promoted to principal, was the first-night Kitri: her glossy technique and equally shiny smile barely compensated for the blandness of her interpretation. Still essentially a soloist, she hasn't yet grasped how to play with a fan or a man.

Galina Stepanenko, more experienced, treated the tricksy choreography as fun. A team player, she responded to the action around her and to her attentive partner, Yuri Klevtsov. They brought the ballet riotously to life after the first night's somewhat stilted account.

The real scene stealers throughout were the old pros - the character dancers. Ilze Liepa, blonde and imperious, quelled the crowd with her castanets; Yulianna Malkhasyants as a gypsy fortune teller foretold trouble with glorious gusto. They and other folkloric specialists showed that Don Quixote has far more to offer than the Royal Ballet's feeble productions have ever realised.