An Introductory Course.- What is a Functional Identity?.- The Strong Degree and the FI-Degree.- The General Theory.- Constructing d-Free Sets.- Functional Identities on d-Free Sets.- Functional Identities in (Semi)prime Rings.- Applications.- Lie Maps and Related Topics.- Linear Preserver Problems.- Further Applications to Lie Algebras.

A functional identity can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The theory of functional identities is a relatively new one, and this is the first book on this subject. The book is accessible to a wide audience and touches on a variety of mathematical areas such as ring theory, algebra and operator theory.