This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian. This subject is intimately connected with a number of classical problems of probability theory such as the summation of independent random variables, martingale theory, and Wiener's theory of polynomial chaos. The book contains a number of older results as well as more recent, or previously unpublished, results. The emphasis is on domination principles for comparison of...