Part 1. Beyond Tonality: From 1900 to World War I

Part 2. Reconstruction and New Systems: Between the Wars

Part 3. Innovation and Fragmentation: From WWII to the Present

This allows for some nuance that a simple list of composers often misses. For instance, Schoenberg's "atonal revolution" is covered in Part 1, along with the "new tonalities" of Stravinsky and Bartok. Part 2 covers the origin of the "twelve-tone system," but makes clear that it did not become influential until years later with the "serial revolution" in France, led by Messiaen and Boulez, in Part 3.

As others have noted, Morgan is not as strong on the more recent period, partly because the book was published in 1991 and thus misses such phenomena as Schnittke's surge of popularity, especially in Russia and Europe, after the collapse of the Soviet regime. I recommend two other books along with Morgan: 1) Gann's "American Music in the Twentieth-Century," which covers developments in the U.S. in greater detail, thus including for instance one of my favorites, Roger Reynolds, and 2) Griffiths' masterful "Modern Music and After," which begins after the Second World War.