Stanley Green's World of Musical Comedy and Musicals Show by Show are both very good for a comprehensive survey of musicals. Ethan Mordden has written a decade by decade series of books about musicals from the 1940s through the 1970s. He's highly opinionated, but enjoyable to read. Ken Mandelbaum's Not Since Carrie is pretty indispensable for a history of flop musicals.
Brooks Atkinson, former theatre critic of the New York Times, also wrote a very enjoyable book, Broadway, about the era of his criticism. There are also several books of collective reviews from the New York Times that are informative. One, called On Stage, I believe, has reviews from the 1920s through the 1970s. I also enjoyed Frank Rich's Hot Seat, which is a collection of his reviews from 1981 to 1994.
You can venture out to some very enjoyable autobiographies...
things like Harvey Sabinson's Darling, You Were Wonderful, Moss Hart's Act One, Cy Feuer's I've Got the Show Right Here, Richard Rodgers' Musical Stages, and if you can deal with more graphic sex than an 8th Avenue porn palace, Original Story by Arthur Laurents. Go to your local library or bookstore and look up books about George Abbott, Josh Logan, Jerome Robbins, Bob Fosse, Michael Bennett and Gower Champion. (Is there a book about Champion? At the very least, try to read up on his staging of Carnival).
I'll try to think of other suggestions.
"Gif me the cobra jool!"