One day in 1964, a New York advertising-jingle composer in his early 30s received an unlikely job offer.

The composer, Mitch Leigh, the Brooklyn-born son of a Jewish furrier from Ukraine, had no theater experience to speak of. All he had ever done was compose incidental music for a couple of short-lived Broadway comedies — “Too True to Be Good” (1963) and “Never Live Over a Pretzel Factory” (1964). Now he was being asked to write the music for a new show that was going to try out at the Goodspeed Opera House in East Haddam, Conn. A few numbers about quests and wine and beautiful women. So Mr. Leigh gave it a shot.

The show, “Man of La Mancha,” opened in New York the next year and ran until 1971, a total of 2,328 performances. It won five Tony Awards, including best composer and lyricist (Mr. Leigh and Joe Darion) and best musical. Richard Kiley originated the dual role of Don Quixote, a doddering gentleman knight with a grand imagination, and Quixote’s creator, the Spanish author Miguel de Cervantes.

Since then, “Man of La Mancha” has appeared on countless stages around the globe (Jacques Brel played the lead in France), has become a staple of American regional theater, has been transformed into a 1972 film starring Peter O’Toole and has enjoyed four Broadway revivals.