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Written by a successful author and respected mathematician, this book emphasizes a concrete and computational approach to the subject of Fourier analysis and wavelet theory while maintaining a balance between theory and applications. In some cases, several different proofs are offered for a given proposition, allowing students to compare different methods. Key Feature Features a wealth of applications to number theory, probability theory, asymptotic analysis, and approximation theory, far beyond what is usually seen in a book at this level. Includes over a dozen graphs of Fourier expansions and related trigonometric sums. Opens each chapter with a preliminary section on motivation and heuristics. Contains more than 200 exercises woven throughout the book. Highlights material that may be considered supplementary to the main themes, making the text suitable for more advanced courses if desired. Table of Contents 1. Fourier Series on the Circle. 2. Fourier Transforms on the Line and Space. 3. Fourier Analysis in Lp Spaces. 4. Poisson Summation Formula and Multiple Fourier Series. 5. Applications to Probability Theory. 6. Introduction to Wavelets. References. Notations. Index.