There are several methods to solve linear and nonlinear partial differential equations. However, these methods are not effective for solving nonlinear partial differential and integral equations involving mixed partial derivatives. Therefore, we focused on developing a new method to obtain exact solutions for these equations with fewer computations and in a shorter time. This method is called the Laplace Substitution Method. We derived the idea for this method from the Adomian Decomposition Method (ADM) and the Differential Transform Method (DTM). In this book, we address initial value problems of nonlinear partial differential and integral equations involving mixed partial derivatives of any order using our developed method, the Laplace Substitution Method. This study includes both linear and nonlinear partial differential and integral equations with mixed partial derivatives.