All the world loves a David and Goliath story, especially when a scrappy little David goes on to become a towering Goliath in his own right. Such is the tale of Joseph Papp, the man who took on City Hall — and the powerful urban planner Robert Moses, and the perhaps even more powerful preconceptions of the cultural ownership of one William Shakespeare — to become a titan of contemporary American theater.

This fall, the very house that Papp built, the Public Theater in downtown Manhattan, will host a play about this homegrown colossus, who was born in Brooklyn in 1921 as Joseph Papirofsky and died in 1991. The work, “Illyria,” written and directed by Richard Nelson, begins in 1958, when Papp was already known as an abiding thorn in the side of the New York establishment.

By that time, he had begun the open-air, free-for-all (in more than one sense) productions that are now known as Shakespeare in the Park. His conversion of the stately Astor Library on Lafayette Street into the New York Shakespeare Festival’s home base was in the future. And Papp, a fighter by nature, still had many battles to go, on many levels, and many opponents to overcome.