Thinking in Jazz: The Infinite Art of Improvisation

This is a fantastic “how” AND “why” book (https://www.lesswrong.com/posts/oPEWyxJjRo4oKHzMu/the-3-books-technique-for-learning-a-new-skilll) for learning jazz. As best I can tell, Mark Levine's The Jazz Theory Book is a good “what” book.

Thinking in Jazz is a well-structured collection of interviews with jazz musicians, focusing on commonalities in their responses. It gives a fantastic insight into where jazz skills come from, what they're made up of, and how many of the world's best practitioners got where they are. I'd strongly recommend the first five chapters to any aspiring musician.