This work is intended to serve as a textbook for a one-year course in stochastic calculus, random differential equations, and their applications. I have endeavored to present a body of knowledge which follows that in an introductory course in stochastic processes and, in my mind, serves a twofold purpose.

The primary objective is to give the reader a working knowledge of random differential equations. In the last twenty to thirty years, the theory of stochastic processes has exerted a profound impact on the modeling and analysis of physical problems. Just as classical differential equations are at the heart of characterizing deterministic physical processes, random differential equations are essential to modern analysis. The study of random differential equations has led to startling advances on practically every front in engineering and science. This impact will certainly continue to be felt.