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This is a survey of the classical Cesro operator aimed at graduate students as well as more experienced researchers. The eleven chapters of the book cover topics from Cesro’s early work on summability of series and continues with the seminal paper of Brown, Halmos, and Shields on the Cesro operator. Along the way, various normality classes of the Cesro operator are covered, as well as invariant subspaces and semigroups. Recent and ongoing work concerning generalizations of the Cesro operator is also included. The book also features detailed endnotes for each chapter with historical references and suggestions for further reading.