BALLET is arguably the most personal of the arts, depending in the first place on the intimate relationship between dancer and teacher, dancer and choreographer. When we watch a great dancer today, we are often no more than a generation or two from, say, the performers of Russia's Imperial Ballet of the 19th century or the great dancers, teachers and choreographers of Serge Diaghilev's Ballets Russes.

Diaghilev's introduction of Russian ballet to the West in 1909, and his artistic sensibility that strove to unite music, dance and decor, enriched all the arts he touched. His Ballets Russes reached a level of innovation and artistic accomplishment great enough to extend an almost personal contact to future generations.

Richard Buckle has already chronicled the lives of both Diaghilev and his star dancer, Vaslav Nijinsky, in superb and exhaustive biographies that are as basic to the literature of the dance as the books of Ivor Guest on the Romantic ballet and Cyril Beaumont on the Russian. Now, in his late sixties, Buckle, one-time ballet critic of The Observer and later of The Sunday Times of London, has also been chronicling his own life in the world of ballet. The present autobiographical volume, In the Wake of Diaghilev, is a fascinating story, fascinatingly told.

"I yearned to devise, inspire or design ballets," he writes. Although he never quite managed that, he has played, for many years, a major role in the life of modern ballet-- through his criticism, his organization of the great Diaghilev Exhibition of 1954 in Edinburgh and London (and many others since), his part in the major sales of precious Diaghilev costumes at Sotheby's in 1968-69, his role as a founder of England's Theatre Museum, and his biographies of Nijinsky and Diaghilev.

The present book is a delight. Buckle's life has brought him in contact with virtually all the contemporary greats of the ballet world and his eye has always been sharply focused on personalities. They are all here. Tamara Karsavina, Nijinsky's beautiful ballerina in the Diaghilev Ballet, holds Buckle's bouquet of flowers in her lap throughout the evening of her 90th birthday party. Serge Lifar, who always wanted to be buried beside Nijinsky and had his corpse disinterred for that purpose, wangles an invitation to a dinner for an exhibition of designs at the Metropolitan Museum of Art; though he had refused to contribute part of his own collection, Lifar nonetheless appropriates both the television cameras and Madame Vera Stravinsky for himself. Romola Nijinsky, widow of the dancer, author of a very misleading biography, source of invaluable information, and constant intriguer, extracts 5 percent of Buckle's royalties in return for her help on his book.

But Buckle views them all, including himself, with humor, and his style varies from the precious ("Many of the best things in life come from the south. . . . To this day . . . I like to write facing Naples.") to the charming, as when he refers to his own "brief candles of comment in The Sunday Times." He once accompanied Rudolph Nureyev and the London Festival Ballet on a tour of Australia and mentions the star's difficulties with backstage dressers who were, he notes, "new to the privilege of serfdom." And his description of a visit from George Cukor, who wanted to make a film about Nijinsky, is nothing less than hilarious.

Buckle's view is always broad and his voice, if occasionally breathless, is always gentle. Above all, the book is filled with an undeniable and obsessive love for the ballet, a knowledge of the larger context of art and cultural life in which it grows, and a constant awareness of the individuals who shape its form and the eccentric personalities that determine its direction.

One of those eccentric personalities was a Kuban Cossack named Vassily Grigorievitch Voskresensky, better known in the west by his adopted name, Colonel W. De Basil, founder of the Ballets Russes de Monte-Carlo. His story and that of his company (actually, an immensely complicated tapestry of different companies, all with constantly shifting personnel) is brilliantly told in De Basil's Ballets Russes by Kathrine Sorley Walker, ballet critic of the London Daily Mail.

Walker notes in her foreword that the story of De Basil and his companies is one of "rivalries, temperaments, intrigues, romance, mystery and obsessive dedication," reminding us once again of the importance of personality. Impresario De Basil and the artists associated with him dazzled audiences for 20 years--in Europe, England, America, Australia--all through the '30s and '40s. The companies revived old works from the Diaghilev repertoire and presented the new work of choreographers Massine, Lichine, Nijinsky and Balanchine, the dancing of accomplished stars like Alicia Markova and Anton Dolin, and the three new stars whose youthful personalities kept the companies vital, the "Baby Ballerinas": Irina Baronova, Tamara Toumanova, and Tatiana Riabouchinska.

But it was De Basil who kept it all going. Directing a ballet company, he once told an interviewer, required "the wisdom of a Solomon, the cunning of a serpent, and the tact of a diplomat." Wisdom and tact," Walker comments, "were not outstanding attributes of his at any time, but he prided himself on his cunning." The composer Nicolas Nabokov called him "the crooked Colonel" and Ren,e Blum, his early partner, called him "the gangster Colonel." De Basil's work, Walker says, was "partisan warfare . . . dedicated to one object--the preservation and presentation of Russian ballet."

Walker has done a marvelous job of narrating the tangled history of the companies from 1931 to 1952, stressing their youthful vitality and special strength in demi-caractMere roles. The text is filled with a rich array of details, anecdotes, and contemporary descriptions, comments and reviews. For this much alone, it will be a basic book for anyone writing about the period. Walker also presents separate chapters on De Basil, on the three Baby Ballerinas and their successors, on the company's tours of Australia, and a particularly illuminating chapter on the company's influence on ballet. Her prose is always clean, her judgments thoughtful, balanced and generous, making De Basil's Ballets Russes a model of ballet history and an essential book for anyone interested in the cultural forces of this century.

When Walker writes of "the marvelous array of personalities who contributed to this company and the wide range of human emotions that motivated its daily life and eventual death," and when Buckle writes of the series of chances and random personal contacts that, luckily, resulted in the founding of the Theatre Museum, on whose research material Walker relied considerably, we are reminded of the fragility of artistic enterprises, and of the debt we owe writers like Walker and Buckle who, by their sheer care and enthusiasm, help to preserve the thing they love.