This book provides an introduction to the central topics and techniques in harmonic analysis. In contrast to the competitive literature available, this book is based on the Riemann integral and metric spaces, in lieu of the Lebesgue integral and abstract topology. This edition has been revised to include two new chapters on distributions and the Heisenberg Group.

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Professor Deitmar holds a Chair in Pure Mathematics at the University of Exeter, U.K. He is a former Heisenberg fellow and was awarded the main prize of the Japanese Association of Mathematical Sciences in 1998. In his leisure time he enjoys hiking in the mountains and practicing Aikido.

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A primer in harmonic analysis on the undergraduate level

Gives a lean and streamlined introduction to the central concepts of this beautiful and utile theory.

Entirely based on the Riemann integral and metric spaces instead of the more demanding Lebesgue integral and abstract topology.

Almost all proofs are given in full and all central concepts are presented clearly.

Provides an introduction to Fourier analysis, leading up to the Poisson Summation Formula.

Make the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups.

Introduces the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.