This volume advances a new method for the solution of game problems of pursuit-evasion, which efficiently solves a wide range of game problems. In the case of 'simple motions' it fully substantiates the classic 'parallel pursuit' rule well known on a heuristic level to the designers of control systems. This method can be used for the solution of differential games of group and consecutive pursuit, the problem of complete controllability, and the problem of conflict interaction of a group of controlled objects, both for number under state constraints and under delay of information. These problems are not practically touched upon in other monographs. Some basic notions from functional and convex analysis, theory of set-valued maps and linear control theory are sufficient for understanding the main content of the book. Audience: This book will be of interest to specialists, as well as graduate and postgraduate students in applied mathematics and mechanics, and researchers in the mathematical theory of control, games theory and its applications.