The Adomian decomposition method (ADM) is a semi-analytical method capable of solving partial and ordinary nonlinear differential equations. This book shows how ADM can be used to solve problems formulated to depict real-life situations in physical world. Through various elaborate examples, ADM is illustrated here as capable of solving all types of differential equations for the series solutions of fundamental problems of physics, astrophysics, chemistry, biology, medicine and other disciplines of science.