Focusing on rings and radicals, this text is part of a series which provides mathematicians and mathematics libraries with surveys of areas undergoing active development, and which reflects the changing distinct areas of pure and applied mathematics.

This book presents a detailed account of the theory of quantaloids, a natural generalization of quantales. The basic theory, examples and construction are given and particular emphasis is placed on the free quantaloid construction, as well as on the perspective provided by enriched categories.