Pinsky (Northwestern U.) offers a self-contained treatment of classical Fourier analysis for upper undergraduate or beginning graduate students who are familiar with the rudiments of Lebesgue measure and integral on the real line. His approach is mostly classical and concrete, preferring explicit calculations to existential arguments. Diligent readers, he says, should be able to complete all of the 175 exercises. He explains Fourier series on the circle, Fourier transforms on the line and space, Fourier analysis in LP spaces, the Poisson summation formula and multiple Fourier series, applications to probability theory, and a gentle introduction to wavelets. Annotation ©2009 Book News, Inc., Portland, OR (booknews.com)