UNDER MY SKIN Volume One of My Autobiography, to 1949. By Doris Lessing. Illustrated. 419 pp. New York: HarperCollins Publishers. $25.

TWO major themes shape "Under My Skin," the first volume of Doris Les sing's autobiography: the twin workings of memory and projection. Why should we suppose that what we remember is more important than what we forget? How is it possible to convey a child's experience of time? Why do memories of childhood grief exert so much more authority than those of joy? And why do we nevertheless entertain extravagant expectations of a life, as she puts it, ever "freer, more honest, more comfortable, always better"?

It is Ms. Lessing's strength that she does not pretend to answer these questions. Rather, she poses them with the vividness of a fine novelist. She gives us an image of child time, for example, with a lice-infested train carriage in the middle of impoverished Russia in 1924, her father helplessly ill with flu, her mother left behind two days before when she stepped off the train to buy food, the little girl dressing and praising her teddy bear, "over and over again, ordering the world, keeping control of events."

Doris Lessing was born Doris Tayler in 1919 in Kermanshah, in what was then called Persia. (A refrain of "what was then called" is one of the devices by which Ms. Lessing creates a picture of the mutating Zeitgeist.) Her mother, trained as a nurse, was devoted to the middle-class values of the British Empire; her father, a book lover and a banker, dreamed of farming. The father had lost a leg in the trenches, the mother a lover. Through Ms. Lessing's childhood the shadow of the Great War hovered "like poison gas," manifested in the pain and bitterness of the maiming, in her parents' obsessive reading about the conflict, in the marital chafing of two people whose mutual commitment could not compensate for the blasting of their disparate ambitions.

WHEN Doris was 4 1/2, the family -- now including a younger brother -- embarked on the precarious overland journey through Russia to reach England, and from there some months later made its way to what was then called Southern Rhodesia in the hope of getting rich. The Taylers built a rough house and began to farm -- first maize, then tobacco. Later, her father tried prospecting for gold, but each new effort failed to make the family fortune. The girl grew up steeped in a sense of exile in her own and other homes, to which people had brought beaded gowns, Liberty print curtains and silver tea services for a life of rigorous poverty under thatch or corrugated tin. It was a world full of lonely women, dispossessed of the gentility they believed their birthright.

The child escaped first into the land. And there would be no way to guess, from the intensity of her attention to its birds and animals, to its smells and to the pleasures of practical accomplishment -- churning butter, sewing, hatching chicks -- that she would become such a dispassionate observer of the wider world.

But partly thanks to her mother's indefatigable pretensions, Doris was sent to one school after another, where she suffered the disciplinary cruelties of the British education system or shrank from the horrifying icons of the convent. She read gulpingly, sensing in that recurrent rhythm both entrapment and exclusion. She converted briefly to Roman Catholicism and, when the spasm passed, shed religion without regret. She grew alert to the contradictions of white Africans, and to the nuances of bigotry that could include her mother's agonized concern over the servants' diet (by current standards an ideal mix of complex carbohydrates) together with her "high desperation" at the inaccurately laid silverware.

Doris's mother, capable and histrionic, resilient and obsessive, a woman who could stand on the deck of a ship in a Force 9 gale but lived in fear of disaster from germs and insects, admonished her daughter to cultivate good sportsmanship and false feeling. Mrs. Lessing speculates thoughtfully on the universality of bitterness in the mother-daughter bond, and seems to effect a reconciliation of her own.

The future writer became aware of several selves. Tigger, who clowned to cover her anxiety, persisted for all the African years in successive manifestations: Tigger Tayler, Tigger Wisdom, Tigger Lessing, Comrade Tigger. There was also a rebel, who evolved out of early adventurousness in the face of parental strictures. And then there was an "Ancient," who appeared when Mrs. Lessing started to write, producing insights of which both Tigger and the rebel would have been incapable.

Mrs. Lessing traveled to Johannesburg and Salisbury, working in a dress shop, as a nursemaid and as a telephone operator; she gloried in her sleek young body, smoked, sewed, danced, went to the movies, got drunk and got married. Europe was again on the verge of war; she was not yet out of her teens. "No point in saying, I will not -- when the Fates are playing war music, dance music." Her marriage to Frank Wisdom produced two children, whom she abandoned a few years later. Mrs. Les sing recounts this passage in her life with complex candor, from the contagious broodiness of young mothers to the self-protective indifference of her own feelings.