Bolshoi problyem!” say my Russian friends, eyes raised to heaven when some difficulty looms. But if the problyem is bolshoi (which means “big” – this being the extent for most of us of our Russian vocabulary), it does not concern the Bolshoi Ballet. Back in London next week, after last summer’s happy visit, the company returns confident, bearing its accustomed gifts of bolshoi stagings, bolshoi dancing, bolshoi aspirations, bolshoi achievements.

It has recovered from past traumas: the collapse of the communist system and with it, unquestioned financial support; the departure of its long-time director Yuri Grigorovich, who had served and survived for 30 years in the Soviet era, both as director (“250 dancers: 250 temperaments,” he said to me) and creator of the bolshoi spectaculars (Spartacus, The Golden Age, Ivan the Terrible) that took the company in triumph round the world.

Able men who were placed in charge of the Bolshoi (Vladimir Vasiliev, Vyacheslav Gordeyev, Alexey Fadeyechev, Boris Akimov) succeeded each other all too swiftly, battling with the tensions of fast-changing political attitudes and the demands of newly emergent market forces, with foreign tours now vital to finance the ensemble. All this was further complicated by the uncertainties of the situation in Russia itself. (One former director asked me: “How can I plan when I only have a one-year contract?”) The fabric of the Bolshoi Theatre itself was in a parlous state, with, inter alia, electrical installations best qualified as antique.

Today, the Bolshoi Theatre sits amid a vast building site as its structure is entirely renewed. I saw it two months ago and marvelled at the extent of the work, the gigantism of the project, the day-long, night-long roar of machinery as the theatre starts to emerge from the surrounding rubble and dust. You see its shape, and the great columns of the façade, although Apollo’s quadriga, which surmounts the pediment, is still in store. And, through all this necessary if exasperating time, the ballet has danced on in Moscow, touring, and using the New Stage, a smaller theatre a street away from the parent building, as its home.

The ballet troupe is, as we saw last summer, in spanking form, and at an intriguing moment (yet another, one might say) in its 230-year history. History is repeating itself, with Russian ballet again opening up to the west for choreographic example, as it did during the 19th century. Balanchine and Forsythe have entered the Petersburg repertory. Moscow also boasts Balanchine works, has acquired Ashton’s La Fille mal gardée, has gained creations by Roland Petit, and will bring to London its new one-act Hamlet-fantasy, Elsinore, commissioned from Christopher Wheeldon this year, and Twyla Tharp’s sneakers-and-point-shoes marathon In the Upper Room, lately staged to loud Muscovite acclaim.

And, with the appointment of Alexei Ratmansky as director, the Bolshoi becomes once again a choreographer’s ensemble – though not exclusively so, as it had been during the Grigorovich era. Ratmansky is a product of its school and company but, uniquely for the troupe, he has danced and choreographed in the west, notably with the Royal Danish Ballet and in North America. His policies for the Bolshoi, as we may judge them over the past three years of his directorate, are astute and imaginative. His fizzing Go for Broke, a version of Stravinsky’s Jeu de Cartes made last year, was the most fascinating choreography I have seen from a Russian creator since Grigorovich’s The Golden Age in 1984, which was a fascinating commentary on the ideals of communism as they had mutated over 60 years.

Ratmansky’s insouciant Bright Stream was very popular last year and returns again this summer to London. This staging showed a concern to examine the early years of Soviet ballet (it rescued a Shostakovich score and a production damned by Stalin in 1935) and some have suggest that Ratmansky plans to resurrect more works from the Soviet era.

It would be unwise and ungrateful to dismiss the 70 years of creativity during the former regime by very considerable choreographers such as Lavrovsky, Vainonen, Zakharov, as merely hobbled and blinkered by communist ideology. The stagings that I saw from this era (and I recall the jolly Miradolina and the blazing Laurencia with great pleasure) were tremendous show-pieces and, much to the point, tremendously danced. The news that Ratmansky is considering a revival of The Flames of Paris – 1789 and its tricolour flags, ardent peasantry, cowering aristos, a splendid score by Asafiev, thrilling dance and drama – is encouraging. Accepting and using its politicised past is a sign of a frankness in the Bolshoi’s policies: history not re-written but understood.

An intriguing parallel is the current desire in both Petersburg and Moscow to look back across the Soviet years to its largely-lost Imperial past. The Mariinsky seeks what are thought to be more “authentic” versions of The Sleeping Beauty and La Bayadère using notations of the Petipa repertory made at the turn of the 20th century. Ratmansky and his colleague Yuri Burlaka have used these same notations (lodged in Harvard’s Theatre Collection) to aid them in reproducing a version of Le Corsaire that, as I reported from its Bolshoi premiere in June, is remarkably successful in suggesting Petipa’s manner, Petipa’s dances.

Like its theatre, the Bolshoi’s ballet is restoring, rebuilding, modernising. And the structure (like the ensemble) remains, in essence, what it ever was: a symbol of Russian artistic genius. Years ago, I met Alexandra Balashova, a ballerina of the Imperial Ballet in Moscow. Much in awe,I asked her to inscribe a photograph to me. She wrote, lengthily: “The theatre is a temple in which I worship every day.” There, even across a century, speaks the Bolshoi Ballet as I know it today.

The Bolshoi season begins on Monday at the Coliseum, London WC2, and runs for three weeks www.eno.org