This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, R). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.