Integer-valued polymials on the ring of integers have been kwn for a long time and have been used in calculus. P@olya and Ostrowski generalized this tion to rings of integers of number fields. More generally still, one may consider a domain D and the polymials (with coefficients in its quotient field) mapping D into itself. They form a D-algebra - that is, a D-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a righ structure, and the very numerous questions it raises allow a throrough exploration of commuative algebra. Here is the first book devoted entirely to this topic. Features: * Thorough reviews of many published works * Self-contained text with complete proofs * Numerous exercises.