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Gian-Carlo Rota was a mathematician who made major contributions to several areas of mathematics. Presented in the first part of this volume are reprints of his papers in analysis which were written at the beginning of his career. These papers on differential equations, operator theory, ergodic theory and other subjects have a continuing and pervasive influence. Reprints of his papers on convexity and probability theory are presented in the second part of the work. These were written towards the end of his career and contain many ideas that have yet to be fully developed. Comprehensive commentaries are included in every chapter. These survey articles detail work inspired by Rota's papers and also include discussions of many unsolved problems. As is customary with Rota's writings, the papers included in this volume - some published here for the first time - contain many fresh and unexpected ideas for further research. Thus, this volume will be of interest to both experts and beginners in the above-mentioned fields.
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Rota's early work was in analysis, more specifically, in operator theory, differ ential equations, ergodic theory, and probability theory. Later, in the 1990's, Rota returned to some of the problems in analysis and probability theory which motivated his work in combinatorics.