Primary subject categories: • Probability theory and stochastic processes • Brownian motionSecondary subject categories: • Stochastic integrals • Stochastic ordinary differential equations (aspects of stochastic analysis) • Transition functions, generators and resolvents • Martingales and classical analysis • Diffusion processes • Continuous-time Markov processes on general state spacesStochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. In this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.3rd revised and extended editionMore than 200 exercisesSolutions includedFor mathematicians, economists, engineers and scientists