Stochastic analysis and stochastic differential equations are rapidly developing fields in probability theory and its applications. This book provides a systematic treatment of stochastic differential equations and stochastic flow of diffeomorphisms and describes the properties of stochastic flows. Professor Kunita's approach regards the stochastic differential equation as a dynamical system driven by a random vector field, including K. Itô's classical theory. Beginning with a discussion of Markov processes, martingales and Brownian motion, Kunita reviews Itô's stochastic analysis. He places emphasis on establishing that the solution defines a flow of diffeomorphisms. This flow property is basic in the modern and comprehensive analysis of the solution and will be applied to solve the first and second order stochastic partial differential equations. This book will be valued by graduate students and researchers in probability. It can also be used as a textbook for advanced probability courses.