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Game theory and contemporary decision theory provide the mathematical foundation of economics. Neuroeconomics, which principally concerns itself with the integrative study of brain, mind and behavior, builds on this mathematical foundation while also drawing heavily from the repository of experimental paradigms that have grown out of economic game theory and behavioral economics. Game theory is central to neuroeconomics primarily because it constitutes a formal mathematical framework with which to bridge insights occurring at different levels of neuroeconomic analysis. In particular, game theoretic principles can be used to express neuroscientific ideas about the brain, psychological concepts regarding the human mind, and economic predictions of human behavior, thereby making these different ideas more rigorously relatable to each other. In this chapter we provide a nontechnical introduction to game theory and its relation to neuroeconomics. It has been written as an overview of the basic concepts most likely to be encountered in neuroeconomic research. The first part of the chapter introduces the reader to the basic concepts and philosophical underpinnings of game theory in relation to neuroeconomics. The second part is an introduction and discussion of common games, including the games featured in the other chapters of this book.