Edward Albee, whose slashing play “Who’s Afraid of Virginia Woolf?” shocked Broadway in 1962 and has since become a classic of American literature, died in his sleep Friday at his home in Montauk.

He was 88.

Albee was the last of the great playwrights of the 20th century, regularly mentioned alongside Eugene O’Neill, Arthur Miller and Tennessee Williams.

He became an overnight sensation when “Virginia Woolf” opened at the Billy Rose Theatre on Oct. 13, 1962. The vicious verbal battles between George and Martha, the alcoholic married couple at the center of the play, shocked critics and audiences.

Albee took the title from a phrase he once saw written on the mirror of a gay bar in Greenwich Village.

Nominated for the Pulitzer Prize, “Virginia Woolf” was rejected by the Pulitzer jury because of its profanity and sexual themes.

Albee later won three Pulitzers — for “A Delicate Balance,” “Seascape” and “Three Tall Women.”

The adopted grandson of legendary vaudeville producer Edward F. Albee, the playwright rejected his comfortable upbringing in Westchester for the bohemian life of Greenwich Village in the 1950s. Disinherited by his parents, he scratched out a living delivering Western Union telegrams while trying to be a writer.

He wrote his first play, “The Zoo Story,” about a violent confrontation between two men in Central Park, on a typewriter he had stolen from Western Union.

“All the short stories and poems and essays I’d written were crap,” he once told me. “I knew that. ‘The Zoo Story’ was the first thing I wrote that ever had any merit.”

It premiered in Berlin in 1959, and opened off-Broadway in 1960 to good reviews.

After the success of “Virginia Woolf” — which landed him on the cover of Newsweek and was later turned into a 1966 film starring Elizabeth Taylor and Richard Burton — Albee wrote a string of controversial, enigmatic and sometimes violent Broadway plays, including “Tiny Alice,” Everything in the Garden,” “All Over” and “The Lady From Dubuque.”

None matched the success of “Virginia Woolf” and by the early 1980s, after critics excoriated his play “The Man Who Had Three Arms,” Albee’s Broadway career was over.

He came roaring back in 1991 with “Three Tall Women,” a searing and darkly funny play about a tough, sometimes nasty woman — a portrait of his mother — at various stages in her life.

“When I got to writing the play, the anger at my adoptive mother was still there, but I added something — a little pity,” he said.

Produced off-Broadway, the play won the Pulitzer, and put Albee back in the spotlight.

Soon he was all over Broadway again with acclaimed revivals of “A Delicate Balance” and “Virginia Woolf” and a new play, “The Goat, or Who Is Sylvia?” — which won the Tony Award.

Of his comeback, he told me, “I never stopped writing plays. People stopped coming to them, but I never stopped writing them. And now they’re coming back. So that’s nice.”