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This book originates from lecture notes for an introductory course on stochastic calculus taught as part of the master's program in probability and statistics at Université Pierre et Marie Curie and then at Université Paris-Sud. The aim of this course was to provide a concise but rigorous introduction to the theory of stochastic calculus for continuous semimartingales, putting a special emphasis on Brownian motion. This book is intended for students who already have a good knowledge of advanceddoi:10.5281/zenodo.4461774 fatcat:jojrvw2osbbwzkxwjk4bvuwqaq