This book is the first comprehensive survey of the field of constraint databases. Constraint databases are a fairly new and active area of database research. The key idea is that constraints, such as linear or polynomial equations, are used to represent large, or even infinite, sets in a compact way. The ability to deal with infinite sets makes constraint databases particularly promising as a technology for integrating spatial and temporal data with standard re- lational databases. Constraint databases bring techniques from a variety of fields, such as logic and model theory, algebraic and computational geometry, as well as symbolic computation, to the design and analysis of data models and query languages. The book is a collaborative effort involving many authors who have con- tributed chapters on their fields of expertise. Despite this, the book is designed to be read as a whole, as opposed to a collection of individual surveys. In par- ticular, the terminology and the style of presentation have been standardized, and there are multiple cross-references between the chapters. The idea of constraint databases goes back to the late Paris Kanellakis.