From the reviews:pThe book under review deals mostly with real-valued functions of a single real variable, but also looks at functions with complex arguments and functions defined on the natural numbers. a ] The material a ] consists of good exposition, illuminating examples, and excellent problems, many from math competitions. a ] this book serves as an excellent introduction to more comprehensive works such as AczA(c)la (TM)s Lectures on Functional Equations and Their Applications. a ] In summary a ] a valuable contribution to the literature of problem solving. (Henry Ricardo, MathDL, April, 2007)Over the years, a number of books have been written on the theory of functional equations. However, very little has been published which helps readers to solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. The student who encounters a functional equation on a mathematics contest will need to investigate solutions to the equation by finding all solutions (if any) or by showing that all solutions have a particular property. Our emphasis will be on the development of those tools which are most useful in giving a family of solutions to each functional equation in explicit form.pAt the end of each chapter, readers will find a list of problems associated with the material in that chapter. The problems vary greatly diffculty, with the easiest problems being accessible to any high school student who has read the chapter carefully. The most diffcult problems will be a reasonable challenge to advanced students studying for the International Mathematical Olympiad at the high school level or the William Lowell Putnam Competition for university undergraduates.pThe modern theory of functional equations can occur in a very abstract setting that is quite inappropriate for the most high school students. However, the abstraction of some parts of the modern theory reflects the fact that functional equations can occur in @H”33333 ¾Û€