An attention-getting writer (novels, Memento Mori. The Ballad of Peckham Rye, The Bachelors, and short stories, The Go-Away Bird) pursues her multi-personae interests, her concern with religion, and her refusal to allow the reader to be at one with her purpose. Here she disperses her story (a loose but provocative thing) over an extended -- and interrupted -- period (thirty years) during which Miss Brodie, (in her prime) holds young minds in thrall, at first in delight at the heady freedom she offers from the rigid, formal precepts of Edinburgh's Marcia Blaine (day) School, later in loyalty to her advanced sedition against the efforts to have her removed. Finally the girls grow up -- and Monica, Rose, Eunice, Jenny, Mary, and Sandy, (particularly Sandy with her pig-like eyes) separate, and the "Brodie set" dissolves- with war, death, marriage, career, and conversion to Catholicism. But there still is a central focus -- who among them betrayed Miss Brodie to the headmistress so that a long-desired dismissal was effective? In this less-than-a-novel, more-than-a-short story, there is the projection of a non-conformist teacher of the thirties, of a complex of personalties (which never becomes personal lives), and of issues which, floating, are never quite tangible. But Muriel Spark is sharp with her eyes and her ears and the craftiness of her craftsmanship is as precision-tooled as the finest of her driest etching. With the past record, the publisher's big push, and The New Yorker advance showing, this stands on its own.