Focuses on the analysis, optimization and controllability of time- discrete dynamical systems and games under the aspect of stability, controllability and (for games) cooperative and non-cooperative treatment. The investigation of stability is based on Lyapunov's method which is generalized to non-autonomous systems. Optimization and controllability of dynamical systems is treated, among others, with the aid of mapping theorems such as implicit function theorem and inverse mapping theorem. Dynamical games are treated as cooperative and non- cooperative games and are used in order to deal with the problem of carbon dioxide reduction under economic aspects. The theoretical results are demonstrated by various applications INDICE Uncontrolled Systems: The Autonomous Case; The Non-Autonomous Case.- Controlled Systems: The Autonomous Case; The Non-Autonomous Case.- Controllability and Optimization: The Control Problem; A Game Theoretical Solution; Local Controllability; An Emission Reduction Model; Dynamical Method for Finding a Nash Equilibrium; Evolution Matrix Games; An n-Person Cost-Game; A Cooperative Treatment of an n-Person