This monograph provides the reader with a comprehensive overview of game theory covering the foundations of the theory of noncooperative and cooperative games, both static and dynamic. It also highlights new trends in cooperative differential games, learning, approachability (games with vector payoffs) and mean-field games (large number of homogeneous players). Based on courses given at the University of Oxford and Imperial College London, this work emphasizes theoretical foundations, mathematical tools, modeling, and equilibrium notions in different environments. The author uses a tutorial style to illustrate the major points so that the reader can quickly grasp the basics of each concept. The comprehensive reference list enables further research. This is the first tutorial to give such a concise and accessible introduction to the subject. It will be of use to all students, practitioners, and researchers looking to understand the basic concepts, models, and applications of game theory.