The ability to draw inferences is a central operation in any artificial intelligence system. Automated reasoning is therefore among the traditional disciplines in AI. Theory reasoning is about techniques for combining automated reasoning systems with specialized and efficient modules for handling domain knowledge called background reasoners. Connection methods have proved to be a good choice for implementing high-speed automated reasoning systems. They are the starting point in this monograph,in which several theory reasoning versions are defined and related to each other. A major contribution of the book is a new technique of linear completion allowing for the automatic construction of background reasoners from a wide range