In this chapter, we will introduce the Nash equilibrium, oneNash equilibrium of the most basic (and famous) concepts in game theory. This concept was formulated, for strategic form games, by John F. Nash [1], who also showed that the mixed extension of every finite strategic form game has a Nash equilibrium. Section 4.1 will give definitions for the Nash equilibrium concept, followed by several examples where the Nash equilibria of the given strategic form games will be calculated using best-response correspondences. This section will also state Nash’s [1] existence theorem (which will be proven in the appendix of this chapter after some mathematical preliminaries). Next, Sect. 4.2 will calculate the Nash equilibria of some well-known strategic form games that were presented in Chap. 1. A short section (Sect. 4.3) will define a strict version of the Nash equilibrium, followed by Sect. 4.4 that will relate the Nash equilibrium of a strategic form game to equilibrium notions that uses dominance. Section 4.5 will introduce the risk dominance concept for two-person strategic form games and Sect. 4.6 will discuss epistemic conditions leading to Nash equilibrium. Finally, Sect. 4.7 will present some mathematical preliminaries and the proof of Nash’s [1] Existence Theorem.