Individuals often make decisions as part of a group. While an individual acting alone can choose as he or she prefers, a collective decision must aggregate the preferences of multiple individuals. Collective decisions may involve as few as two people, such as a couple deciding where to eat dinner, or several members voting in a committee, hundreds of members voting in a legislature, or millions of people voting on a referendum or electing a parliament or president. Any such decision – except perhaps an informal decision in a small group – requires a clearly defined rule to aggregate diverse individual preferences and identify the social choice; for example, the proposal or candidate to be selected. Yet different rules have different properties, and they may produce different social choices even for the same individual preferences. Broadly understood, social choice theory identifies, analyzes and evaluates rules that may be used to make collective decisions. So understood, social choice is a subfield within the social sciences (especially economics and political science) that examines institutions that may be called ‘voting rules’ of various sorts. More narrowly understood, social choice theory is a specialized branch of applied logic and mathematics that analyzes abstract objects called ‘preference aggregation functions’, ‘social welfare functions’ and ‘social choice functions’. While this Handbook includes several chapters that introduce the reader to social choice theory in its narrower sense, we included the word ‘voting’ in the title to signal that it covers the field in its broader sense.