In this chapter we introduce three families of choice rules that play important roles in social choice theory, namely, social welfare functions, social choice correspondences, and social choice functions, and we investigate their basic properties, such as Pareto optimality, anonymity, neutrality, and monotonicity. The study of social welfare functions culminates in Section 2.2 with Arrow's Impossibility Theorem. The study of social choice correspondences and functions focuses on monotonicity properties and leads to the conclusion that every strongly monotonic social choice function whose range contains at least three alternatives is dictatorial (see Theorem 2.4.11). The Gibbard-Satterthwaite Theorem is shown, in Section 2.5, to be a corollary of the preceding theorem. Simple games and their basic properties are defined in Section 2.6. We conclude with a proof of Nakamura's theorem on cores of simple games (see Theorem 2.6.14).