Dead Poets Society, a new play written by Tom Schulman, the screenwriter for the 1989 film that starred Robin Williams, Ethan Hawke and Robert Sean Leonard, is a deft, engaging stage version superbly directed by John Doyle for his first production as the artistic director of Classic Stage Company. The story, set in 1959 in a boys’ prep school, Welton Academy, follows a half dozen young men whose lives are affected by John Keating, an English professor. Keating is the kind of teacher who believably inspires his students and urges them to think for themselves rather than unquestioningly follow the rules adults have set out. In its way, Dead Poets Society is a veiled attack on the dangers of fascism that resonates particularly since the election.