This latest issue of Zygmund's classic treatise includes a foreword by Robert Fefferman of the University of Chicago. Professor Fefferman describes Zygmund's mathematical development, his contemporaries and, of course, the man himself. He has set this book in context and given an insight into how Zygmund's work has influenced contemporary mathematics. Professor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of developments in trigonometric series, Fourier series and related branches of pure mathematics since publication of the original edition. The two volumes are here bound together. Volume I, containing the completely rewritten material of the original work, deals with trigonometric series and Fourier series - auxiliary results: Fourier coefficients - elementary theorems on the convergence of S[f ] and S[f ]; summability of Fourier series; classes of functions and Fourier series; special trigonometric series; the absolute convergence of trigonometric series; complex methods in Fourier series; divergence of Fourier series; Riemann's theory of trigonometric series. Volume II provides much material previously unpublished in book form, and covers trigonometric interpolation; differentiation of series - generalized derivatives; interpolation of linear operations - more about Fourier coefficients; convergence and summability almost everywhere; complex methods; applications of the Littlewood-Paley function to Fourier series; Fourier integrals; a topic in multiple Fourier series.