This book examines space tether systems – one of the most forward thinking directions of modern astronautics. The main advantage of this technology is the simplicity, profitability and ecological compatibility: space tethers allow the execution of various manoeuvers in orbit without costs of jet fuel due to the use of gravitational and electromagnetic fields of the Earth. The authors discuss the modern state of the space tether’s dynamics, with specific attention to the research projects of the nearest decades. The book presents the most effective mathematical models and the methods used for the analysis and prediction of space tether systems’ motion; attention is also given on the influence of the tether on spacecraft’s motion, to emergencies and chaotic modes.