This book is distributed by Elsevier Science on behalf of Science Press. Available internationally for the first time, this book introduces the basic concepts and theory of the stability of numerical methods for solving differential equations, with emphasis on delay differential equations and basic techniques for proving stability of numerical methods. It is a desirable reference for engineers and academic researchers and can also be used by graduate students in mathematics, physics, and engineering. It has an emphasis on the stability of numerical methods for solving delay differential equations, which is vital for engineers and researchers applying these mathematical models. It introduces basic concepts and theory as well as basic techniques for readers to apply in practice. It can be used as for graduate courses or as a reference book for researchers and engineers in related areas. It is written by leading mathematicians from Shanghai Normal University in China.