This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book covers classic topics but also more recent topics of game theory. The book proposes numerous exercises with detailed solutions. The difficulty of the exercises is variable so that both undergraduate as well as postgraduate students finds exercises adapted to their needs. The author was teaching game theory for more than 20 years and he/she likes studying how his/her undergraduate, postgraduate and post-doctoral students play games. The book tells that game theory is a very open, very stimulating research field. It shows strategies with specific properties: by defining new, well-founded, specific properties, and sheds new light on interactive behaviours. The book presents concepts in the spirit of the perfect and sequential equilibria, but also quantal behaviour and replicator equations. It discuses recent topics in game theory, best reply matching, regret minimization, level-k reasoning, and also on forward induction.