The book is devoted to a promising technology for contactless removal of space debris, dubbed “ion beam shepherd”. A brief analysis of various aspects of the space debris problem is carried out. Different methods and technologies for space debris mitigation and removal are considered. To simulate and study the motion of the “shepherd” and the space debris object during its contactless de-orbiting, dynamic models are presented. Simplified analytical models have been developed to calculate the ion beam impact. A method to determine the force transmitted by the plasma plume of an ion thruster to an orbital object immersed in it using its central projection on a selected plane is proposed. Algorithms and results of numerical calculations of the forces and torques transmitted by the ion beam to the upper stages of the “Cyclone-3” and “Cyclone-4” launch vehicles are given. The control system to maintain the necessary position of the “shepherd” relative to the space debris object is designed and analyzed. The evolution of the space debris orbit was analyzed taking into account the necessity to switch-off the ion thrusters in the shaded areas of the orbit. The expediency to use control actions for increasing the eccentricity of the orbit is investigated. The book may be of interest for research and engineering staff working in the field of rocket and space technology, as well as for undergraduate and graduate students studying in the relevant areas.