This is the first of a two-volume set that provides an introduction to non-cooperative Game Theory. Volume 1 covers the basic concepts, while Volume 2 is devoted to advanced topics.This volume is divided into two parts: Part I deals with games with ordinal payoffs, while Part II covers games with cardinal payoffs. In each part we discuss both strategic-form games and dynamic games. This volume is relatively short (approximately 260 pages) and richly illustrated with approximately 200 figures. It is suitable for both self-study and as the basis for an undergraduate course in game theory as well as (together with Volume 2) a first-year graduate-level class. It is written to be accessible to anybody with high-school level knowledge of mathematics. At the end of each chapter there is a collection of exercises accompanied by detailed answers. Volume 1 contains approximately 90 exercises.