Delay partial difference equations occur frequently in the approximation of solutions of delay partial differential equations by finite difference methods, random walk problems, the study of molecular orbits and mathematical physics problems. Many results have been done for the qualitative theory of delay partial difference equation in the past ten years. But there has not been a book in the literature presenting the systematical theory on delay partial difference equations so far. This book provides a broad scenario of the qualitative theory of delay partial difference equations. The book is divided into five chapters. Chapter 1 introduces delay partial difference equations and related initial value problems, and offers several examples for motivation. In Chapter 2, we first discuss the oscillation of the linear delay partial difference equations with constants parameters, where the characteristic equations play an important rule; then we present some techniques for the investigation of the oscillation of the linear delay partial difference equations with variable coefficients. Chapter 3 is devoted to the study of the oscillation of the nonlinear delay partial difference equations. In Chapter 4, we consider the stability of the delay partial difference equations. In the last Chapter, we introduce some recent work on spatial chaos. Most of the materials in this book are based on the research work carried out by authors, their graduate students and some other experts during the past ten years. Readership: Advanced undergraduates, graduates and researchers in applied mathematics, computation mathematics, physical and biological sciences.