An overview of twentieth-century compositional styles -- Pitch centricity and composition with motivic cells -- Pitch centricity and symmetry -- Introduction to pitch-class set theory -- Analyzing atonal music -- Drawing on (and reinterpreting) the past -- And inventing the future -- Twelve-tone music I : an introduction -- Twelve-tone music II : invariance, symmetry, and combinatoriality -- Serialism : developments after 1945 -- Expanding the limits of musical temporality -- Aleatory music, sound mass, and beyond -- Where past and future meet -- Simplifying means -- Into the twenty-first century.