The overall aim of this book is to provide a rigorous means to characterize the micro structure and properties of heterogeneous materials that can simultaneously yield results of practical utility. A unified treatment of both micro structure and properties is emphasized. The book is divided into two parts. Part I deals with the quantitative characterization of the micro structure of heterogeneous via theoretical, computer-simulation and imaging techniques. Emphasis is placed on theoretical methods. Part II treats a wide variety of effective properties of heterogeneous materials and how they are linked to the micro structure. This is accomplished using rigorous methods. Wherever possible, theoretical predictions for the effective properties are compared to available, experimental and computer-simulation data. This book will be of interest to graduate students and researchers in applied mathematics, physics, chemistry, micro structure science and engineering.