IT'S HARD TO KNOW how to refer to the subject of Judith Thurman's absorbing biography. She was born Karen Christentze Dinesen in 1885; she was called at different times and by different people Tanne (her family nickname), Osceola (her first literary pseudonym), Tania, Titania, Jerie and, by her later literary disciples, Pellegrina, Amiane, or Scheherazade. Her official married name was Baroness von Blixen-Finecke, otherwise Karen Blixen. Her last writing name was Isak Dinesen. Her biographer states that "these names had their own etiquette, logic and geography. They were separate entrances to her presence, varying in grandeur and accessibility." Thurman uses them all, according to context; at times her poetic logic defies analysis, as when within two pages her heroine is called Tanne, Tania, Karen Blixen, and Dinesen.

The crucial period of Karen Blixen's life, her time in Africa, will be familiar to readers of her Letters from Africa 1914-1931, edited with a good deal of additional information by Frans Lasson and published here last year. The childhood, however, turns out to be equally crucial for understanding her inflated sense of her own destiny. Her father was a wanderer, who knew American Indians as she was to know Africans. She was his favorite child: they made "an aristocracy of two." Already a fantasist, being singled out by her father gave her "an exaggerated view of her erotic power." He hanged himself when she was 10, leaving her with a terror of being abandoned and a strong sense of being something very special. She became a sharp-tongued, self-centered, bookish girl, too clever for the aristocratic men of "conspicuous virility" to whom she was attracted in her native Denmark.

She fell in love with one of these -- her Swedish cousin Hans von Blixen-Finecke. It was his brother Bror that she married: "one of the most durable, congenial, promiscuous, and prodigal creatures who ever lived," according to Thurman. Within a year of marriage, in Africa, he had given her syphilis, probably picked up from a Masai woman in whose tribe the disease was endemic. Bror, chronically unfaithful, seems to have been untroubled by symptoms; but for the rest of her life Karen Blixen was tortured by illness, crippling pain, debility, and a growing inability to eat. Bror's casual management of their coffee farm brought financial ruin, and the family shareholders put Karen Blixen in charge on condition he keep away. They were divorced in 1922, against her will.

Her relations with the Africans were paternalistic, satisfying her benevolent despotism; she loved them, says Thurman, as a lonely child loves her dolls. She loved too the farm, the Ngong hills, the whole way of life: "here is where I ought to be." She also loved the dashing Englishman Denys Finch Hatton, who came and went as he chose, infinitely charming and infinitely detached. Her longing for something more permanent had already made a breach betweem them before the disaster in which he was killed in his own plane, just at the time when the family was refusing to subsidize her farm any longer and summoning her home. She lost everything she wanted in the space of a few months.

Judith Thurman is a poet and journalist: her book is "written" in the artistic sense, as many academic biographies are not. She has steeped herself in her subject over seven years, taken the trouble to learn Danish, and had access to the vast archive of letters, family documents and manuscripts at the Royal Library in Copenhagen. These factors give the book both its virtues, which predominate, and its faults. It is at certain points overwritten, as if the author's total immersion in Isak Dinesen's theatrical personality had affected her judgment and sense of humor. It is for example a little grandiose to suggest that the story of a spectrally thin Dinesen disembarking on her return from Africa with her stockings spiralling down her legs, and then cheering up when her brother supplies her with an effective pair of garters, "offers a glimpse of that delicate system of symbolic weights and counterweights that governed her moods."

With a mass of detailed material at hand, there was no room for an assessment of Dinesen's achievement and place as a writer -- a topic, the biographer says, in any case outside her purpose and competence. The works are considered in the context of career-history and for their biographical interest; Thurman points out that the remarkable book Out of Africa is no documentary but, in part, "a sublime repair job," salvaging pain and failure as well as celebrating happiness. For critical comment, Thurman leans on Robert Langbaum's The Gayety of Vision: Isak Dinesen's Art (1965). Now that the life is known in all its gallantry and enormity, it would be good to have more modern criticism of the work. "Genius" of some kind is taken for granted here.

Genius in the sense of "daemon" Dinesen certainly had. She emerges as a monster of vitality. Even as a child she told her sisters such long stories that they begged her to stop. She never wrote her work down until she had it off by heart, like an ancient bard; and in later life, as a celebrity, would talk for hours in a trance-state, exhausting her audiences. She was moody, demanding and unreasonable, an ancient mariner.

The last third of the book describes how, like some medieval witch, she took over the lives of successive young male disciples, involving them in erotic, metaphysical folies Ma deux. She owed her staying power to amphetamines, and her physical survival to Clara Svendsen, who came as cook and stayed as secretary, companion, nurse, translator and finally literary executor. Her manic energy and her belief in her own magical powers lived on in a frail, skeletal body; in the late 1950s she was electrifying New York and like Edith Sitwell, another sibylline figure, being photographed with Marilyn Monroe. When she died in 1962, the cause of death was emaciation, due to malnutrition.

This is a "gothic tale" worthy of the author of Seven Gothic Tales, the book that first made Isak Dinesen famous in the United States. Judith Thurman's account of this tremendous, terrifying person and her background and influences points up how little most of us know about Scandinavian history, culture or literature. But after reading about her, one feels it was no coincidence that Hamlet was a Dane.