This book is a systematic and comprehensive approach to functional equations as a whole. Unlike in other branches of competitive mathematics, there is very little theory; instead, the methods and techniques utilized in solving these equations play the most important part. For this reason the book takes a highly practical path and includes lots of problems designed to teach students how to familiarize themselves with every strategy employed, as well as how to experiment in combining and manipulating different techniques. This work contains all the important functional equations given at contests in recent years, classified by the way the equations are solved. It explains the reasoning behind each method and offers advice on how to invent meaningful solutions. A publication of XYZ Press. Distributed in North America by the American Mathematical Society. Readership Middle and high school students interested in mathematics competition preparation. Table of Contents  Cauchy's equations
 Generalized Cauchy equations
 Reducing to Cauchy
 Substitutions
 Symmetrization and additional variables
 Iterations and recurrence relations
 Constructive problems
 The D'Alembert equation
 The AczélGołáSchinzel equation
 Arithmetic functional equations
 Binary and other bases
 Geometric functional equations
 Approximating by linear functions
 Extremal element method
 Fixed points
 Functional equations for polynomials
 Functional inequalities
 Miscellaneous problems
 Hints and solutions
 Notation and abbreviations
 Bibliography
