There are history books as in textbooks and any number of them will do the trick. I think the one I had was called "History of Theater" and had a red cover. It starts with the Greeks and goes from there.
If you're looking for American Theatre, try "Broadway" by Brooks Atkinson. That will take you up to the 50s and 60s when Broadway was the center of theatre in America, before the rise of regional theatre.
Atkinson was the longtime drama critic for the Times and as was written once, is the reason there is a Brooks Atkinson Theatre on Broadway.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher