This book details one of the most innovative concepts in space flight: tethered space systems. These involve connecting satellites in orbit around Earth using thin cables called tethers. There are a number of interesting applications for this concept, such as energy production from the interaction between the system and the magnetic field of the Earth, momentum transfer for a satellite, microgravity laboratories, and the space elevator. The text presents several models, focusing on the simplest but most important system, which consists of two satellites in orbit around the Earth. The authors derive equations of motion and describe methods of analysis.