This treatise deals with modern theory of functional equations in several variables and their applications to mathematics, information theory, and the natural, behavioural and social sciences. The authors have chosen to emphasise applications, though not at the expense of theory, so they have kept the prerequisites to a minimum; the reader should e familiar only with calculus and elementary algebra, and have a basic knowledge of Lebesgue integration. Where, for certain applications, more advanced topics are needed, the authors have included references and explained the results used. Moreover, the book has been designed so that the chapters can be read almost independently of each other, enabling a selection of material to be chosen for introductory and advanced courses. At the end of each chapter are included exercises and further results, some 400 in all, which extend the material presented in the text and also test it. The history of functional equations is well documented in a final chapter which is complemented by an encyclopedic bibliography running to over 1600 items.