Surely, Antoni Zygmund's Trigonometric Series has been, and continues to be, one of the most influential books in the history of mathematical analysis. Therefore, the current printing, which ensures the future availability of this work to the mathematical public, is an event of major importance. Its tremendous longevity is a testimony to its depth and clarity. Generations of mathematicians from Hardy and Littlewood to recent classes of graduate students specializing in analysis have viewed Trigonometric Series with enormous admiration and have profited greatly from reading it. In light of the magnitude of Antoni Zygmund as a mathematician and of the impact of Trigonometric Series, it is only fitting that a brief discussion of his life and mathematics accompany the present volume, and this is what I have attempted to give here. I can only hope that it provides at least a small glimpse into the story of this masterpiece and of the man who produced it.
Antoni Zygmund was born on December 26, 1900 in Warsaw, Poland. His parents had received relatively little education, and were of modest means, so that his background was far less privileged than that of the vast majority of his colleagues. Zygmund attended school through the middle of high school in Warsaw. When World War I broke out, his family was evacuated to Poltava in the Ukraine, where he continued his studies. When the war ended in 1918, his family returned to Warsaw, where he completed pre-collegiate work, and entered Warsaw University.