Description logics (DLs) are used to represent structured knowledge. Inference services testing consistency of knowledge bases and computing subconcept/superconcept hierarchies are the main feature of DL systems. Intensive research during the last fifteen years has led to highly optimized systems that allow to reason about knowledge bases efficiently. However, applications often require additional non-standard inferences to support both the construction and the maintenance of knowledge bases, thus making the inference procedures again incomplete.This book, which is a revised version of the author's PhD thesis, constitutes a significant step to fill this gap by providing an excellent formal foundation of the most prominent non-standard inferences. The descriptions given include precise definitions, complete algorithms and thorough complexity analysis. With its solid foundation, the book also serves as a basis for future research.