Machine generated contents note: 1. Space tether systems: review of the problem -- 1.1. Application of space tether systems -- 1.2. Chronology of experiments with the use of space tethers -- 1.3. Materials for tether production -- 1.4. Study of space tether dynamics: state of the problem -- 1.5. References -- 2. Mathematical models of space tether systems -- 2.1. Simple models of space tether system consisting of two point masses connected by a massless tether -- 2.2. Simple model of a space tether system consisting of two point masses connected by a heavy tether -- 2.3. Model of a space tether system with a heavy flexible tether -- 2.4. Model of a space tether system consisting of a point mass connected by a heavy tether with a rigid body -- 2.5. Model of a space tether system consisting of two rigid bodies connected by a heavy elastic multipoint tether -- 2.6. References -- 3. Motion of a spacecraft with a tethered payload -- 3.1. Mathematical model of a base spacecraft with a tethered payload -- 3.2. Analytical solution in case of a slow changing of the parameters -- 3.3. The approximate analytical solutions in the variables of the amplitude-phase -- 3.4. Analytical solutions for small oscillations -- 3.5. Estimation of the microaccelerations level on board the spacecraft -- 3.6. Motion of the spacecraft with a propulsion system -- 3.7. Motion of a spacecraft around its centre of mass in a circular orbit with a vertically deployed elastic tether -- 3.8. References -- 4. Delivery of a payload from an orbit by means of a space tether -- 4.1. Tether deployment schemes -- 4.2. Project YES2 -- 4.3. Modelling of the YES2 tether deployment -- 4.4. Abnormal situations during tether deployment -- 4.5. References -- 5. Use of methods of chaotic dynamics for the analysis of tether system motion -- 5.1. Some elements of chaotic dynamics -- 5.2. The chaotic approach in STS dynamics -- 5.3. References