This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. Each section outlines basic solution methods for the differential equations in that section. The text presents equations and their applications in areas such as differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, and wave theory. This handbook is essential for researchers, engineers and students of applied mathematics, mechanics, control theory, and the engineering sciences.