In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the "Cours d'analyse", to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the "Cours d'analyse". For this translation, the authors have also added commentary, notes, references, and an index.