A WIDER WORLD. Portraits in an Adolescence. By Kate Simon. Harper & Row. 186 pp. $14.95.

WITH A COMPLETELY unsentimental eye, Kate Simon, well- known for her literate and lively travel guides, looks back upon her adolescence in New York during the Great Depression. Just as it is unnecessary to be Jewish to enjoy Levy's rye bread, one needn't have lived through the 1930s on the edge of poverty in the Bronx to appreciate Kate Simon's evocation of a milieu short on jobs and cash but full of a variety and vitality unknown to the grim, striving yuppies of the 1980s. College in particular tended to be liberating. Since unemployment or a series of scruffy jobs were high probabilities after graduation, why not major in music, oriental languages, philosophy, art history, or anything else that caught one's fancy? College was no way-station to a professional career.

Kate was on consistently bad terms with her father, who wanted her to drop out of school as soon as possible, get a full time job, attract suitable Jewish suitors, marry and replenish the earth. By the time she was 15, she had left home and, from the proceeds of assorted part-time jobs, managed to support herself as a roomer or in tiny apartments while she finished high school and entered Hunter College. She recalls teachers who encouraged her, introduced her to art, music and poetry and, on occasion, made lesbian advances. Obviously she was the sort of talented, rebellious, high-spirited youngster who triggers the managerial impulses of teachers on the hunt for prot,eg,es.

Her adventures brought her to Harlem in the company of the only prostitute whom she then or later knowingly encountered. She was rescued by a black man who diagnosed her condition of virginity, escorted her to the subway, and warned her that if he saw her again he would give her a worse beating than any her father might be impelled to administer. For a time, she shared a tiny apartment and a bed with the tenderly recalled Davy who was as frightened of sex as she was. In due course, she became pregnant not once but twice with the cooperation of males more intrepid than Davy. Right-to-lifers could read with profit what it was like to get a cheap abortion without anesthesia. "Around and around I went, pain to madness with pain, to death with ceaseless, forever, pain."

ADOLESCENCE HAD its moments of comedy. The rich Sandra Rubenstein for whom she worked had a plan for her. She was to marry the unattractive son of the family and proceed to have babies. The first infant would remain with her, the next would be transferred to the Rubenstein daughter, Kate Simon's friend, who was too frail herself to contemplate childbirth -- and so on with all subsequent children. Understandably Kate rejected a career as a one-woman maternity ward. Then there was the elderly Italian who mitigated his loneliness with the sexual favors of his goat; the radical Bergsons and their summer colony of fellow believers; and the great lover Jones who did his energetic best to replicate Brigham Young's polygamy. At the urging of Kate's favorite teacher, who served as one of Jones' wives and financiers, Jones was appointed to initiate Kate into sex. Unfortunately he was physically unattractive and much given to boring discourse featuring the fecundity of nature and his own contribution to nature's cause. During an idyllic episode in the woods designed to culminate in her deflowering, Kate prudently fell asleep.

Somehow within this context of hard, badly-paid work and sexual adventure, the author became an educated woman. But "the girl who was to be immortal, the bright fantasist and loony wanderer" was not quite lost. She "carried an envelope of earlier shapes" around with her: "Lie an old string of beads slipped from their broken thread, like a loose pile of fading snapshots, they rattle around with the golden Borsalino hat and the volume of Heine verse in a box rarely opened but palpably there."

This is a beautifully written memoir, a sequel to Bronx Primitive: Portraits in a Childhood. I went to high school in the Bronx for a time during the 1930s and lived for a season on the Grand Concourse, recalled by the author as the Champs Elys,ees of the borough. Now changed much for the worse, art deco apartment houses are defaced by graffiti; Loews Paradise, that temple of the cinema complete with organ and starry ceilings, is a routine multiplex; and the Concourse Plaza, site of numerous expensive weddings and bar mitzvahs, now houses welfare families. I look forward to the next installment of Kate Simon's recollections.