Sonny Rollins estimates that even in the 21st century, the music of Coleman Hawkins ‘is in everybody that’s playing saxophone’. The instrumental technique Hawkins developed for the tenor saxophone has been adopted, in some way or the other, by most jazz saxophonists. But Hawkins was also a master of the theoretical principles governing tonal music and of their application within the confines of improvised swinging music. This second aspect of his technique is the subject of this thesis, which deals principally with four parameters: rhythm, harmony, melody, and development. Chapter 1 presents Hawkins’s ties with Western classical music, his improvisational method, and his role as an influential model for an approach to jazz improvisation fo...