When the student of engineering or applied science is first exposed to stochastic processes, or noise theory, he is usually content to manipulate random variables formally as if they were ordinary functions. Sometime later the serious student becomes concerned about such problems as the validity of differentiating random variables and the interpretation of stochastic integrals, to say nothing of the usual worries associated with the interchange of the order of integration in multiple integrals. It is to this class of readers that this book is addressed. We attempt to analyze problems of the type just mentioned at an elementary yet rigorous level, and to adumbrate some of the physical applications of the theory.