ELIA KAZAN A Life <i> by Elia Kazan (Anchor Books / Doubleday: $12.95) </i>

Elia Kazan, the distinguished director of stage (“Death of a Salesman,” “Streetcar Named Desire”) and screen (“Splendor in the Grass,” “On the Waterfront,” “East of Eden”) tells his life story with candor and fury. For years there was, in his words, “self-betrayal”--the product of the rites of assimilation of a Greek immigrant from Turkey. But having hidden a lifetime’s deep resentment behind his Anatolian smile, Kazan now sets the record straight: “The fact is that I am mad, almost every morning. I wake up mad. Still.”

One of the century’s most important directors, Kazan’s reputation was tarnished by his appearance in 1952 before the House Un-American Activities Committee when he admitted that he had once been a Communist and volunteered the names of eight other former Group Theater members who had also been Communists. In this memoir, he attempts to defend what he did against the harsh criticism he received but eventually admits that he may have been wrong.

Kazan’s other claim to notoriety, and the book’s most lively sections, were his innumerable infidelities--in alleyways, in the back rows of movie-theater balconies, on park benches. He tells us he was Marilyn Monroe’s intermittent lover.

“This is strong stuff,” Richard Eder wrote in his review, “and so is the book as a whole. (It is) lightened by some remarkable perceptions and a wealth of anecdote.”