Krasovskii's Extreme Shift Control Principle and Its Applications Yuri S. Osipov Russian Academy of Sciences, Moscow, Russia Arkady V. Kryazhimskiy IIASA, Austria / Steklov Mathematical Institute, Russia e-mail: kryazhim@iiasa.ac.at In the beginning of the 1970s, N. N. Krasovskii proposed a new method of closed-loop control of dynamical systems affected by uncertain nonobservable disturbances -- the extreme shift control principle. In the next decades that principle has developed into one of the fundamentals of the theory of closed-loop differential games. The present lecture discusses the role of the extreme shift control principle within and beyond that theory including its applications to problems of robust inversion of control systems, constrained optimization problems, and problems of exact stabilization of uncertain dynamical systems.