This second edition has been enlarged and considerably rewritten. Among the new topics are infinite product spaces with applications to probability, disintegration of measures on product spaces, positive definite functions on the line, and additional information about Weyl's theorems on equidistribution. Topics that have continued from the first edition include Minkowski's theorem, measures with bounded powers, idempotent measures, spectral sets of bounded functions and a theorem of Szegö, and the Wiener Tauberian theorem. Readers of the book should have studied the Lebesgue integral, the elementary theory of analytic and harmonic functions, and the basic theory of Banach spaces. The treatment is classical and as simple as possible. This is an instructional book, not a treatise. Mathematics students interested in analysis will find here what they need to know about Fourier analysis. Physicists and others can use the book as a reference for more advanced topics. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Graduate students and research mathematicians interested in harmonic analysis. Reviews "...this volume can be an excellent way to get one's feet wet and see whether it is worthwhile to take the plunge. The book has helpful and challenging exercises for the reader. It should be emphasized that the great strength of the book lies in the large number of interesting special results it contains. Many of the prettiest facts of harmonic analysis are on display here in a very attractive setting."  Bulletin of the American Mathematical Society Table of Contents  Fourier series and integrals
 The Fourier integral
 Discrete and compact groups
 Hardy spaces
 Conjugate functions
 Translation
 Distribution
