This book is a comprehensive introduction to the stability of functional equations in several variables. It covers classical results as well as current research in the field. The book is the first to present an integrated and self-contained treatment of the subject. It includes chapters on approximately additive and linear mappings, the stability of quadratic functional equations, generalizations using the method of invariant means, approximately multiplicative mappings, the stability of trigonometric and similar functions, functions with bounded nth differences, approximately convex functions, the stability of generalized orthogonality functional equations, stability and set-valued functions, stability of stationary and minimum points, functional congruences, quasi-additive functions, and related topics. It also includes references and an index. The concept of stability of functional equations in several variables originated over half a century ago when S. Ulam posed a fundamental problem, and Donald H. Hyers provided the first significant partial solution in 1941. The subject has been developed by an increasing number of mathematicians, particularly in the last two decades. Three survey articles have been written on the subject by D.H. Hyers (1983), D.H. Hyers and Th. M. Rassias (1992), and most recently by G.L. Forti (1995). None of these works included proofs of the results discussed. A sad note: during the final stages of the manuscript, our beloved co-author and friend Professor Donald H. Hyers passed away. We express our grief and sorrow that he was not able to see this completed work. This book is dedicated to his memory. The authors thank Stefan Czerwik, P. Gavrutä, Soon-Mo Jung, Jürg Rätz, Wilhelmina Smajdor, Józef Tabor, and Jacek Tabor for their useful suggestions and comments. They also thank Haim Brezis for his help and encouragement. They wish to acknowledge the superb assistance provided by Ann Kostant of Birkhäuser Boston in the publication of this book, as well as the support by L.L.C.F. The author also thanks Elizabeth Loew of T£Xniques, Inc. and Tom Grasso of Birkhäuser Boston for their aid throughout the typesetting and production process.This book is a comprehensive introduction to the stability of functional equations in several variables. It covers classical results as well as current research in the field. The book is the first to present an integrated and self-contained treatment of the subject. It includes chapters on approximately additive and linear mappings, the stability of quadratic functional equations, generalizations using the method of invariant means, approximately multiplicative mappings, the stability of trigonometric and similar functions, functions with bounded nth differences, approximately convex functions, the stability of generalized orthogonality functional equations, stability and set-valued functions, stability of stationary and minimum points, functional congruences, quasi-additive functions, and related topics. It also includes references and an index. The concept of stability of functional equations in several variables originated over half a century ago when S. Ulam posed a fundamental problem, and Donald H. Hyers provided the first significant partial solution in 1941. The subject has been developed by an increasing number of mathematicians, particularly in the last two decades. Three survey articles have been written on the subject by D.H. Hyers (1983), D.H. Hyers and Th. M. Rassias (1992), and most recently by G.L. Forti (1995). None of these works included proofs of the results discussed. A sad note: during the final stages of the manuscript, our beloved co-author and friend Professor Donald H. Hyers passed away. We express our grief and sorrow that he was not able to see this completed work. This book is dedicated to his memory. The authors thank Stefan Czerwik, P. Gavrutä, Soon-Mo Jung, Jürg Rätz, Wilhelmina Smajdor, Józef Tabor, and Jacek Tabor for their useful suggestions and comments. They also thank Haim Brezis for his help and encouragement. They wish to acknowledge the superb assistance provided by Ann Kostant of Birkhäuser Boston in the publication of this book, as well as the support by L.L.C.F. The author also thanks Elizabeth Loew of T£Xniques, Inc. and Tom Grasso of Birkhäuser Boston for their aid throughout the typesetting and production process.