San Francisco Ballet, one of the oldest, biggest and most prestigious American companies, was last here eight years ago; their return – to judge by the buzzing crowd packing out Sadler’s Wells last night – has been eagerly awaited. Fortunately, they are not wasting a moment of their stay, treating the capital’s ballet fans to nine performances in as many days and showing ten works in total over three different mixed programmes.

On Friday night – opening night – we saw Programme A, featuring George Balanchine’s Divertimento no. 15 from 1956, and two recent commissions for San Francisco Ballet: Edwaard Liang’s Symphonic Dances (2012) and Christopher Wheeldon’s Number Nine (2011). The combination of these three works felt like a masterclass in triple bill design: over an evening of just the right length, we saw the perfect proportions of continuity and contrast in everything from choreography, to music, to costume and lighting design, all realised with tremendous verve and skill by the talented personnel of the company’s different departments.

Balanchine’s Divertimento no. 15 started the evening on a note of precise, intricate classicism – and that was just the orchestra, whose spirited rendition of the Mozart score would have graced any chamber music festival with honour. The other elements of the piece followed the music, so we had bright overhead lighting, traditional tutus in sherbet lemon and baby blue, and Balanchine setting fiendishly fast variations mostly composed of the lightning-quick beats, low jumps and controlled turns collectively known in ballet as petit allegro. To execute this chorography well you need a rock-solid classical training and, despite a few initial wobbles, the artists of San Francisco Ballet left us in no doubt that they had the requisite technique in spades – not to mention quite a bit of panache. The last movement is relentless for all the dancers, and must be exhausting to perform, but there was not a hint of strain on show: on the contrary, the women seemed barely to be touching the ground, and the men achieved impressive elevation above it.

Symphonic Dances, by Edwaard Liang, offered an almost complete contrast. In place of Mozartian restraint there was Rachmaninov doing big Russian emotion; in place of stiff pastel net there was near-liquid burnt-orange chiffon; in place of stage-flooding overhead light there were the intense shadows of side-lighting. Where Balanchine used diagonal formations, tight port-de-bras, and distant, almost polite partner work, Liang had his dancers on the straight axes of the stage, and showcased twisting arms, multiple changes of level, and intensely connected pas de deux. The company really seemed to hit their stride in this piece – which was made for them only this season – and the full range of their impressive abilities became apparent. To a dancer immensely strong and flexible, they executed Liang’s demanding, flowing moves with a complete physical mastery that left them enough resources to be as tender, playful, lyrical or passionate as the choreography demanded. Liang had such a beautiful sense for the drama and emotion in Rachmaninov’s music, not to mention a real flair for conveying relationships and an impressive repertoire of twisting, passionate lifts, that I would love to see his take on a major story ballet. His skilful interweaving of an intense pas de deux and a small group of female dancers in the waltz would be perfect for the ballroom scene in Cinderella; when he made his male dancers pop with high-spirited bravura, they might have wandered out of the fight scenes in Romeo and Juliet (which he has also choreographed this year). The audience at Sadler’s Wells loved every minute, and gasped with delight at the final, audacious tableau.

Christopher Wheeldon’s 2011 commission for San Francisco Ballet, Number Nine, rounded off the evening with sixteen minutes of sheer joy. The colours made the strongest impression: the floor was Yves Klein blue, the corps de ballet canary yellow, the soloists violet, orange, lime green and turquoise; the backdrop royal blue or crimson depending on who was dancing in front of it (it felt like a lesson on the colour wheel). Michael Torke’s music was baroque and energetic and Wheeldon’s choreography matched – the movement was constant, but every position, however briefly held, was totally precise. The dancers, again, were superb – the breathtaking elevation of their cabrioles made me scribble in my notebook ‘are they all under 25?’ What an absolute, exhilarating delight they are to watch; I guarantee you everyone in that audience left wreathed in smiles.

Tickets are still available for some of the San Francisco Ballet performances this week: do yourself a favour and snap one up. This display of American talent really is unmissable.