The book deals with certain algebraic and arithmetical questions
concerning polynomial mappings in one or several variables. Algebraic
properties of the ring Int(R) of polynomials mapping a given ring R into
itself are presented in the first part, starting with classical results
of Polya, Ostrowski and Skolem. The second part deals with fully
invariant sets of polynomial mappings F in one or several variables,
i.e. sets X satisfying F(X)=X . This includes in particular a study of
cyclic points of such mappings in the case of rings of algebrai
integers. The text contains several exercises and a list of open
problems.