Professor Zygmund’s “Trigonometric Series,” initially published in Warsaw in 1935, swiftly became a classic in the field. The first edition offered a concise overview of the primary findings known at the time, albeit constrained in detailed discussion. A substantially expanded second edition (Cambridge, 1959) released in two volumes comprehensively incorporated advancements in trigonometric series, Fourier series, and related areas of pure mathematics since the original publication.

Bound together with an introductory note from Robert Fefferman, these two volumes illuminate the significance of the text. Volume I, featuring a completely reworked version of the original material, delves into trigonometric series and Fourier series. Volume II introduces substantial content that was previously unavailable in book form.

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