Tao (mathematics, U. of California-Los Angeles) presents the material he used in a graduate course summarizing the nascent field of quadratic--and more generally higher-order--Fourier analysis. He focuses on the foundational and preparatory aspects and on the simplest illustrations of key results in order to provide a companion to the core literature, which is often quite technical and lengthy. Readers are presumed to have a graduate-level familiarity with basic real analysis and measure theory, particularly the soft or qualitative side. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)