This book presents papers in the general area of mathematical analysis as it pertains to probability and statistics, dynamical systems, differential equations, and analytic function theory. Among the topics discussed are: stochastic differential equations, spectra of the Laplacian and Schrödinger operators, nonlinear partial differential equations which generate dissipative dynamical systems, fractal analysis on self-similar sets, and the global structure of analytic functions.

"The material here presented represents an elaboration on my Colloquium Lectures delivered before the American Mathematical Society at its September, 1940 meeting at Dartmouth College." - Preface.