Alma Schindler was born (Aug. 31, 1879) with one of the most respected family names in Vienna. Her father was "the most celebrated landscape painter of the era," and he obviously instilled in her a taste for alliances with men of distinction. Three of the most distinguished became her husbands: Gustav Mahler, internationally famed in his lifetime as a conductor and today as a composer; Walter Gropius, who founded the Bauhaus school and made it a major force in 20th-century art and architecture, and poet-novelist Franz Werfel, author of such books as "The Forty Days of Musa Dagh" and "The Song of Bernadette."

Besides her three husbands, she was an intimate (sometimes platonic) of innumerable others. Some of Gustav Klimt's mature paintings bear a strong resemblance to the picture of Alma Mahler on the cover of Karen Monson's biography--a striking, statuesque figure, somehow remote and imperious, looking vaguely like a fragment of an ancient icon. The reason is possibly that Alma made that kind of impression on Klimt during a tempestuous, inconclusive flirtation while she was still in her teens.

Another painter, Oskar Kokoschka, portrays a very different Alma in his 1914 double portrait, "Die Windsbraut" ("The Tempest"), which is reproduced and described in Monson's book: "On a swirling, luxuriously colored bed, a woman--Alma--lies with her head on Oskar's shoulder, appearing much larger than he. She sleeps peacefully, covered only by billowing fabric. Fully suited, he is sharply awake, gazing anxiously into the distance, sharing none of her rest." A mural he painted for her home showed "Alma rising toward heaven in fiery immolation while he stayed below in Hell, engulfed by serpents." These are mementos of a torrid love affair after Mahler's death, characterized by his "irrational and impossible dependency." It reached a point where Kokoschka's mother threatened Alma "to release her dependent lover by a certain date, or be shot." After her marriage to Gropius, Kokoschka lived for a time with a life-size doll made in her image, whose "death" at a wild party attracted the interest of the police.

These are only a few instances with particularly illustrious names. Alma Mahler was proposed to, shortly after Gustav's death, by a doctor who had attended him in his final illness. Other serious attachments included Alexander von Zemlinsky, who was Arnold Schoenberg's composition teacher as well as her own; Ossip Gabrilowitsch, the pianist and conductor; composers Franz Schreker and Hans Pfitzner, and dramatist Gerhart Hauptmann. There was also a prominent Viennese priest who had a small apartment where they spent a lot of time together.

All of her marriages, in one way or another, developed their own forms of unhappiness. With Mahler, Alma was the self-sacrificing helpmate to a genius; her assignment was to create and preserve an environment in which his creativity could flourish undisturbed. Her own work as a composer (a promising beginner) must cease in deference to the higher claims of his creativity. She once warned him that she would love him "only until someone stronger came along," and he replied, "I cannot imagine anyone stronger."

With Gropius, the problem was remoteness--compounded by World War I, which kept him away from home most of the time. They had a daughter, Manon, but Alma also bore a son (who died in infancy) to Werfel while Gropius was at war. When her husband became aware of the situation, he accepted it with the dignity that was one of his basic qualities. He even intervened with the police to help Werfel when he became involved in revolutionary activities in the last days of the war. Alma still fantasized sometimes about Kokoschka and wrote in her diary, "The name Gropius lies on me like a piece of barbed wire. I am not Gropius and thus cannot be called by that name. My name is Mahler, for eternity." The divorce was long delayed, while various a trois arrangements were tried, chiefly because both parents wanted custody of Manon, who finally stayed with her mother. She died of polio at 19; Alban Berg (the subject of an earlier biography by Monson) wrote his Violin Concerto in her memory.

Alma did not marry Werfel until 1929, 11 years almost to the day after she had borne his son. He was probably the most congenial (if not the most inspiring) of her husbands and their marriage was her longest, lasting until his death. Their life was disrupted by the rise of Hitler, who banned her first husband's music and her third husband's books. They became refugees, and some of Monson's most vivid pages deal with their problems trying to leave Europe after the fall of France. When they reached America (ultimately Hollywood, where he became involved with the film industry), the pangs of exile were compounded by financial pressures and Franz's declining health. His death recalled many other personal losses, which Alma summed up in a short, eloquent phrase when she was asked to attend his funeral: "I never go."

Monson has done exhaustive research on this fascinating life, and she retails her accumulated facts in an orderly, readable style. Still, there is an unanswered question: How did Alma manage to fascinate so many spectacularly and diversely talented men? No clear answer emerges, and there were probably a variety of answers. To Mahler, who was nearly 20 years older, Alma represented youth and vitality; to Werfel, who was 11 years younger, she may have been more of a protective mother figure. A key ingredient was undoubtedly her combination of striking appearance and quick intelligence.

She may actually have been fortunate in contracting a childhood case of measles that left her hearing impaired--for conversation, not for music. "She taught herself to compensate in social situations," Monson explains, "by paying rapt attention to the person who happened to be nearest to her--usually one of the male persuasion--making him feel as if he were the only other one in the world."