FREUD, A LIFE FOR OUR TIMES; By Peter Gay; Norton; 810 pages; $25.

Of the two names, Karl Marx and Sigmund Freud, that hover over the 20th century and its revolutionary upheavals, it is likely that Freud's has proven the most profoundly unsettling.That is because, in his effort to "map the mind," Freud changed not only the way we think about others and about society but also how we see the most intimate ways we understand ourselves, as well.

Author Peter Gay shows in this large, sympathetic biography of the man and the movement how that came about. Gay is himself perhaps the most outstanding cultural historian of the Victorian and early modern era, as well as a studied psychoanalyst.

Gay finds the complex drives that made Freud in what he calls the "bewildering texture" of Freud's familial relationships, which Freud both confronted and evaded as he developed, refined and revised his map of the mind.

For example, Freud's study, "Totem and Taboo," was published in 1913 when Freud was 57 and psychoanalysis at least moderately well-established. Gay notes that the work, "like so much else in Freud's work . . . productively translated his most intimate conflicts and his most private quarrels into material for scientific investigation."

In a straightforward chronology, Gay traces the complex path Freud followed. He divides Freud's work into three major sections the foundations, between 1856 and 1905; the elaborations, until 1915; and the revisions that continued until Freud's death in 1939.

He parses in remarkably lucid prose each of the major works and the famous case histories, showing how they both extended Freud's theory of the mind and their role in his campaign to make psychoanalysis acceptable.

As Gay shows repeatedly, Freud was a man of complexity and even contradictions. A cultural conservative and proper 19th century bourgeoise in manners, dress and even behavior, Freud also saw himself as a radical social critic but "in the domain of sexuality alone."

Perhaps nowhere was Freud's contradictory nature more apparent than in his view of women, about whom his theories were as often wrong as right. Freud knew his views would prove unpopular and Gay does not try to mask their offensiveness.

Freud's work on female sexuality is among his most unsatisfactory. Still, his movement and there is no doubt in these pages that it was his movement was one in which women, with his encouragement, made major contributions.