THE JAZZ THEORY BOOK -- Mark Levine
The Jazz Piano Book -- Mark Levine
The first has served as a solid introduction to jazz for a lot of people here, myself included. There no other books I know of that serve as a serious foundation for people who come to jazz with some significant pre-existing ability on their instrument already. There are about a dozen complete tunes laced through the book in increasing order of difficulty, plus hundreds of fragments from tunes. Tunes are presented in quite reasonable order, from least to most difficult.
I'm not a pianist, so I can't speak directly to the Jazz Piano Book, but it's consistently spoken of well around here. You'd need this one to learn how to comp.
And the Real Book, 6th edition. This one, specifically:
For better or worse, the standard point of reference for jazz standards.