Database research in the last decade has increasingly focused on providing support for non-standard applications. One important domain refers to the representation and processing of spatial information, as needed, for example, in geographical information systems. Database systems with additional capabilities for managing spatial information are called spatial database systems. This book deals with appropriate modeling and implementation of concepts for geometry in spatial database systems. Spatial data types provide a fundamental abstraction for modeling the structure of geometric entities, their relationships, properties, and operations. This selfcontained monograph for the first time gives an extensive survey of this research field and introduces a new, general, and sophisticated framework for the formal definition and robust implementation of spatial data types. The work is centered around the ROSE algebra which offers general types to present points, lines, and region features together with a comprehensive set of operations. The design of the spatial algebra is based not on Euclidean geometry but on a discrete geometry basis called a realm. This book is a must for anybody interested in geographical information systems, spatial data modeling, or spatial database systems.