This book explores the background of a major intellectual revolution: the rigorous reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his contemporaries in the first part of the 19th century. Their generation changed the calculus from a method of solving problems to a collection of theorems, based on precise definitions, about limits, continuity, series, derivatives, and integrals. The book shows how Cauchy reshaped inherited 18th-century concepts to create an approach to rigor that we still accept today. In so doing, The Origins of Cauchy's Rigorous Calculus provides fresh insights and a new perspective on the foundations of analysis.