The objective of this textbook is to provide the mathematical models and algorithms needed to develop a thorough understanding of all control system functions of a rigid body spacecraft. Relatively simple, but practically applicable algorithms are presented rather than recent advances. We try to avoid detailed and specialized issues that are of less importance for the fundamental understanding, such as detailed environment models, etc. Furthermore, control problems that can be cast in standard formulations and solved with existing methods are not treated here. Instead, we intend to provide an understanding of the principles, put them in an engineering context, and try to give all explanations as concise as possible. Besides conventional three-axis attitude control systems, the following topics are treated in this book:• Control of agile rotation maneuvers using control moment gyros • Precise pointing control with error classes for pointing instruments • Control systems with accelerometers and free-flying test masses, which provide low-disturbance or disturbance-free environments We believe that these topics are of considerable relevance for the design of future spacecraft control systems, especially in the field of science and Earth observation missions.