Gunther Schuller presents a thorough musical analysis of the early history of jazz, from starting with its roots in west African music, ragtime, and the country blues. The bulk of the book covers the 1920's, ending with the start of the 1930's as the last rough edges of New Orleans jazz have been smoothed and the orchestras of Ellington and Basie perfected the big-band swing style. It must be emphasized that this is a musical analysis, heavy with notated examples from the recordings of the era, and thus would not be accessible to those without some musical training. Schuller truly analyzes the music on every single level, illustrated examples range from the "shape" of a single note to the structure of an entire piece and covering all scales in between. While of course no two people have the same taste in music, Schuller does an excellent job of highlighting the best pieces from the important musicians of the time; even the best musicians in the 1920's were forced to record a lot of bland pop and corny vaudeville/minstrel music, so it's quite useful to have a guide to help sift the gems from the duds.
There are a few complaints to be had. There are certainly errors in some of the transcriptions, though this is to be expected in transcribing by ear such complex music. Additionally, I thought the organization of the book could have been a little better; for example he analyzes Louis Armstrong's Hot Five period in great detail early on in the book, and discusses how this music marked the end of the dominance of the New Orleans style in jazz. Yet the very next chapter is focused on Jelly Roll Morton, whose career consisted of nothing but the New Orleans style! That being said, there is a lot of music to be covered in this book and there is likely no perfect way to organize all of the material.
A few faults aside, this is absolutely essential reading for anyone with musical background looking to learn about the roots of jazz.