Persons' attitudes are typically formed in interpersonal environments in which influential positions on issues are in disagreement and liable to change. Our investigation focuses on the formation of attitudes, including shared attitudes and consensus, in groups whose members are communicating their positions on an issue. The communication of an attitude to others may occur in various ways, including spoken or written communication (via an expression of opinion, belief, or preference) and nonverbal communication (via overt behavior, a subtle gesture, or a facial expression). An influential communication, in which one person's attitude affects another's, is an endogenous interpersonal influence, whereas all other effects on attitudes are exogenous influences on the attitudes. The attitudes that are being shaped by these influences may deal with any object about which group members can express a positive or negative evaluation – particular issues, places, persons, events, institutions, symbols, or beliefs. When persons are modifying their attitudes in response to information about the attitudes of other group members, and these other members are doing the same thing, flows of interpersonal influence are generated that permit important indirect effects of members' attitudes on the attitudes of others via intermediaries. In this chapter, we formally present social influence network theory as a mathematical model of endogenous interpersonal influence on attitudes that takes into account the network of such influences.