Game theory is a mathematical discipline that deals with the modeling and the analysis of interactive decision situations. Such situations involve several decision makers that have different goals, and the decision of each one of them may affect the other decision makers. The theory originated in the 1940s, and since then it has been applied in many areas , like economics, biology, computer science, and political science. The book is especially well adapted to teaching: classical mathematical results are presented with mathematical completeness and rigor. The teacher will find all the material necessary for a mathematical understanding of the theory, without any need to use other sources. In addition, the book is replete with exercises of varying levels of difficulty, starting with easy exercises for beginners and ending with difficult ones suited for Ph.D. students.