ΒΙΒΛΙΟ: The Quest for Functions - Functional Equations for The Beginners (pdf)

Functional equations is a rather popular topic at the IMO and other mathematical competitions, both national and international. At least 19 IMO-problems can be classified as functional equations and all these problems are listed below. 

The question posed in this type of problems is to find all functions satysfying the given equation and, possibly, some additional conditions like continuity, monotonicity or being bounded.

Click here.