Game theory analyzes strategic interactions, which are fundamental in all social sciences. It assumes goal-oriented actors such as individuals or organizations that meet certain rationality requirements. In evolutionary game theory, these restrictive assumptions are dispensable. Evolutionary game theory is not only important for biology, but also for social sciences. Although it does not involve inheritance in the biological sense, it does involve cultural and social evolution. Social norms and institutions, behaviors, cultural patterns, linguistic idioms, organizational structures, technical innovations, and ideas can spread through learning and imitation. During imitation, “errors” or mutations may occur. Successful strategies (e.g., a social norm or institution) are imitated more frequently, while unsuccessful strategies disappear. The dynamic process may eventually result in an equilibrium that can be analyzed using the tools of evolutionary game theory. The concept of an “evolutionarily stable equilibrium” or ESS plays a key role in this. This article outlines some basic features of the analysis of equilibria in evolutionary game theory.