This book gives a comprehensive treatment of stochastic approximation algorithms using their differential equation limits, which lays bare its dynamical aspects. Highlights of the book include a streamlined treatment of classical results such as the analysis of asymptotic behavior for decreasing and constant stepsizes and the functional central limit theorem, and inclusion of several important extensions and recent developments such as concentration bounds, avoidance of traps, stability tests, asynchronous implementations, differential inclusion limits, multiple time scales, and general noise models. In addition, major applications are surveyed category-wise, with special focus on stochastic gradient descent. The book will be a valuable resource to students, researchers, and practitioners in statistics, applied probability, control and communication engineering, operations research, machine learning, and economic models. Contents: 1 Introduction 2 Convergence Analysis 3 Finite time bounds and traps 4 Stability Criteria 5 Stochastic Recursive Inclusions 6 Asynchronous Schemes 7 A Limit Theorem for Fluctuations 8 Multiple Timescales 9 Constant Stepsize Algorithms 10 General noise models 11 Stochastic Gradient Schemes 12 Liapunov and Related Systems 13 Topics in Analysis 14 Ordinary Differential Equations 15 Topics in Probability