Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. P@olya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain D and the polynomials (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, thisring 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