When I reached the final chapter of Jennifer Homans's history of ballet, I knew that, sadly, it would come to dominate not the book  it's a throwaway 10 pages, a tiny percentage of the text  but the public perception of it. Homans wrote it as an elegiac epilogue and in it gently suggests that classical ballet may be over, its creations only on museum display. All we'll now hear about Apollo's Angels is the media circling it like the jilted Willis in Giselle, wittering "Whither?" Yet what matters most about Homans's truly original work is the previous four centuries and hundreds of pages. And in those, ballet repeatedly became rigid or span into chaos  only to revive itself.

After all, what we mean by "classical" ballet is romantic ballet, merely the last-but-one reinvention. When Louis-Philippe was proclaimed king of France after the July revolution of 1830, he privatised the Paris Opéra under a manager who set out to profit by propping the place up. One of its first productions, in 1831, was Meyerbeer's opera Robert le Diable, which had the obligatory ballet sequence. The house was darkened; the scenery had a diorama effect; and the dancing, dead nuns tore off their habits to reveal white dresses, like the garb of pure girls in post-1789 republican festivals.

The mother superior of this corps of corpses was the most stupendous novelty, the ballerina Marie Taglioni, who was a summary of the history of dance so far, and a revolution in herself. Her father had trained in the formal dance manners of anciens régimes across Europe. His daughter was plain and stubby, with round shoulders. No curls, no smiles. Taglioni flogged herself like a drayhorse for six hours a day, mastering everything her father knew and experimenting with stunts from Italy, where men and women were hoicking themselves up on their toes, even their toe points, no mean feat in satin slippers faintly stiffened with rows of darning stitch. Taglioni beefed up her calves and sinewed her back so she could not merely pose on demi-pointe, but flit that way, could leap as high as a man, yet seem modestly feminine. Her conflicting discipline and freedom, effort and apparent effortlessness, self-determination and reticence made her the sensation of Robert le Diable. The next year, her father created La Sylphide for her. We know it only in a tasteful Danish rewrite, but the Taglioni original drove poets demented and made her the mobile embodiment of romanticism. After Taglioni, women stole ballet from the male dancers who had dominated it since its court beginnings in the 16th century.

Taglioni is Homans's heroine: Homans was a dancer, and has practised all the styles she describes, from the basic positions of civil politesse notated at the Sun King's Versailles to Kenneth MacMillan's knotted, chopped postures. The opening 540 pages follow dance's interlinked yet geographically separate directions, pursuing questions Homans asked when young  for example, why is the technically perfect St Petersburg/Leningrad Kirov so unlike the Moscow Bolshoi? Her answer is a miniature history of Russia from imperial Francophilia, with St Petersburg reprising Versailles, through to post-Stalinist, yet still emphatically Soviet, Muscovite mores. "Which country has the best ballet?" Nikita Khrushchev boomed as the Bolshoi toured the US, and went on to swagger that ballet was the USSR's glorious pride (alas soon to include the Bolshoi's grinding, gaudy Spartacus). In an aside of genius, Homans points out that ballet is the last bastion of the reforms that Napoleon legislated across the lands he controlled and conquered, "professional rigour and a meritocratic ethic joined to military-style discipline". In ballet, Bonaparte never retreated from Russia.

Homans assigns a chapter to each conjunction of zeitgest and location. By the time she reaches Taglioni's Paris years, France was almost at the end of its dance-power, except for its export of the grand manner to Russia, and its import from Russia, a century later, of Diaghilev's company and its sublimely un-, even anti-, grand manner. Italy's braggadocio gave Taglioni her edge, indirectly. And at La Scala, Milan, in 1881, the extravaganza Excelsior opened with the Spanish inquisition and closed with a tunnel blasted through the Alps, all performed in unified motion by an ensemble of 500, plus two cows and an elephant; it became the global hit progenitor of Busby Berkeley movie routines and the Beijing Olympics spectaculars. The Danes went beyond their de-romanticised Sylphide to formulate a blond-wood ballet style with a social and educational aesthetic that continues to this day, while the British hosted two centuries' worth of émigrés, guesting on stages high and low.

Mostly low, as among the earliest of the Russians to star in London was Anna Pavlova, unflummoxed at sharing an upmarket music hall with a Bioscope kinematograph short. Lydia Lopokova did vaudeville turns in America before settling in Bloomsbury as the wife of JM Keynes. Homans casts the economist, along with Marie Rambert and Ninette de Valois, as the establishment pas de trois of English ballet. Homans seldom puts a foot wrong over social class, so her British section is a perfect divertissement. It's serio-comic: Frederick Ashton's nostalgic gestures; the conventual austerity of Sadler's Wells; the pairing of Margot Fonteyn and Kirov-trained Rudolf Nureyev, after he fled the inglorious USSR  both, writes Homans, were conservatives, surest with the prerevolutionary repertoire. "It was not just that Nureyev made Fonteyn young again, they also stayed old together."

For most of the 20th century, the greatest Russians created their ballets in the US. Sometimes they were in denial of Russian-ness through most of their lives, as was Jerome Wilson Rabinowitz, Jerome Robbins, born in New York to old country immigrants. He escaped a job in a corset factory to hoof on Broadway and then in 1939 was coached in the part of Petrouchka by Mikhail Fokine, who had first choreographed it almost 30 years before for Nijinsky. Vera Stravinsky, wife to its composer, thought Robbins a more heartbreaking, more Russian Petrouchka than Nijinsky. The other great American choreographer, George Balanchine, who is Homans's adored hero, lived and died accepting his origins as Georgi Melitonovitch Balanchivadze, servant of the tsar, grateful recipient of a pre-1917 St Petersburg training supervised by those who had premiered The Nutcracker and The Sleeping Beauty, works of the Romanovs' ballet master Marius Petipa. Then over 60 years, Balanchine created his own diverse American company and devised 400 ballets for it and everybody else, and also numbers for Hollywood and Broadway shows.

For Balanchine, Petipa and Tchaikovsky had never exited the stage, but he also venerated New World dance as incarnated in Fred Astaire's balance of practised ease and innate nobility. (I imagine the devoutly Russian Orthodox Balanchine hung a still of Fred in mid-leap on his personal iconostasis.) Balanchine's spirit of grace borrowed from Astaire's semblance of nonchalance, for when anyone expecting narrative or fancy metaphor asked Balanchine what his ballets were about, he "liked to respond, 'About 28 minutes'". For Homans, that wisecrack encapsulates Balanchine's Apollonian certainties that ballet had universal as well as human physiological laws: it is a religion, and one of love.

I read the Balanchine chapter the morning after I'd seen the Royal Ballet in his Theme and Variations  Petipa's St Petersburg to Tchaikovsky's music. He'd made it in 1947 for Alicia Alonso, a ballerina who had endured several operations for failing sight that confined her to bed, where she learned major roles by "dancing" them within her immobilised body, both a reversal and a manifestation of Balanchine's maxims "don't think, just dance" and "be in the now". At the end of the evening's bill, Alonso, almost 90, now blind, glided on to the Covent Garden stage to take that last curtain call for herself, for Balanchine, for Taglioni (whom she revered). Also for classical ballet? I don't believe it, quite. The audience wasn't heading for the exits. Anyway, what a show it had been.

Jennifer Homans's history of the art, culture and political context of ballet is like a beautiful painting in a slightly askew frame. She is a former dancer who trained at the School of American Ballet in New York, and was the wife of the historian Tony Judt, who died in August. She exchanged the stage for academia two decades ago but one can still tell from her prose the kind of dancer that she was: meticulous, devoted and, au fond, profoundly romantic.

But her passionate identification with her subject leads Homans to a fatalistic conclusion. "For those of us who were there at the end of the last great era, and who experienced its vigour and its decline, the change has been momentous," she writes in her introduction and 550 pages later confesses that: "After years of trying to convince myself otherwise, I now feel sure that ballet is dying we are watching ballet go."

Is this the measured judgment of a social historian or the lament of an American dancer for whom, as for many of her colleagues and compatriots, the lights went out in 1983 with the death of George Balanchine? She is both things at different times and she has strongly held opinions which, as in the case of her peremptory dismissal of Kenneth MacMillan, verge on the chauvinistic.

Ballet, she writes, "is an art of high ideals and self-control in which proportion and grace stand for an inner truth and elevated state of being". That such an art must redefine itself for an era as cynical and fragmented as our own is a truth that she acknowledges, but she has little patience for those attempting the task. Balanchine and Ashton make the cut, but MacMillan is dismissed pretty much out of hand.

By the end, Homans writes, MacMillan "had reduced ballet's eloquent language to a series of barely audible grunts". Such a reductive verdict is unworthy of a writer of her sophistication. Some of MacMillan's experiments failed, but others succeeded gloriously, and in damning him for attempting to take ballet into new territory while simultaneously bewailing the art form's incipient demise, she demonstrates only that she, not ballet, has run out of steam.

There has probably never been a time in the past 200 years when it was not at least half true to say that most choreography "veers aimlessly from unimaginative imitation to strident innovation"; one can imagine Théophile Gautier murmuring as much to Jules-Henri Vernoy de Saint-Georges in the foyer of the Paris Opéra in 1840.

If she takes a dim view of ballet's living practitioners, Homans writes with translucent beauty and authority of its lost past. She takes us back "to the religious and humanist origins of ballet: back to the Great Chain of Being, to angels and the harmony of spheres, to the court of Louis XIV and the strict aristocratic etiquette that had first given ballet its forms". From the Enlightenment and the story-ballet, she sweeps us to the late-1700s and the French Revolution. Here, at the Paris Opéra, was born the first modern corps de ballet, a group of maidens in white, the colour of revolutionary purity and virtue, whose role on stage was an essentially ethical one: to represent the community and the nation. Eventually, these maidens were "picked up and transformed in the imaginations of Romantic poets and writers and given canonical form in La Sylphide and Giselle".

Insights like this give Homans's history profound resonance and it's only rarely that her contextualising looks forced. Few would disagree that the 19th-century ballerina Marie Taglioni "fused the elegance and refinement of a lost aristocratic past with a new and airy spirituality", but to say that her dancing "seemed to echo a more general and pressing desire for reconciliation" in the wake of the Bourbon restoration is probably stretching a point.

The case that Homans makes wholly convincingly, in the case of Taglioni and others, is that the great dancers and choreographers of the 18th to the 20th centuries succeeded at least in part because of their ability to reproduce the "emotional tone" of the eras in which they lived. Her description of Balanchine's 1957 ballet Agon, arguably the most important dancework of the 20th century, is a tour de force, but she anchors it in hard fact. Originally danced by Arthur Mitchell, who was black, and the "pale and icily detached" Diana Adams, the ballet premiered "at a critical juncture of the civil rights movement less than three months after the riots at Little Rock high school in Arkansas".

That she fails to bring the same macro-micro gaze on our own times, and has nothing to say about such choreographers as Alexei Ratmansky, William Forsythe or Wayne McGregor is a pity, for they reproduce, just as surely as the dead masters, the emotional tone of our own day. And any analysis of ballet which fails to mention China or Japan, almost certainly the seedbeds of the next classical dance-boom, is wilfully self-limiting.

But then almost everything that Homans the cool-eyed historian tells us refutes the conclusion of Homans the bereft dancer. For what she demonstrates is that ballet abides. That it marks time, it vamps until ready. And then, in scintillant and unexpected form, is reborn.