Tradition! by Barbara Isenberg (2014)

Subtitled: The Highly Improbably, Ultimately Triumphant Broadway-to-Hollywood Story of Fiddler on the Roof, the World's Most Beloved Musical.
 
Highly readable and light story of the making of Fiddler on the Roof, from conception to film to revivals all around the world. 

Filled with lots of little gems about the theater world, from personalities like Jerome Robbins and Zero Mostel (always fascinating) to the fact that Chaim Topol was only in his 30s when he filmed the movie, Isenberg even mentions Lin-Manuel Miranda's using Fiddler as inspiration not only for In the Heights, but for his wedding dance. 

Dishy and interesting, but still poignant and beautifully conveys the universality of the show.