The volume deals with the question of regularities in the course of sociocultural evolution. The evolutionary process of societies is defined as the generation of social roles and their relations; a role is understood as a pair of social rules and role specific knowledge. Accordingly evolution is the growth of cultural knowledge and the development of a network of social roles. These theoretical assumptions are clarified and tested via a mathematical model, i.e., a sociocultural algorithm (SCA). Computer simulations show that the evolutionary course of societies is determined by an evolutionary parameter, that is the degree of differentiation or role autonomy respectively. An additional model of cognitive ontogenesis is provided; it can be shown that cognitive ontogenesis and sociocultural evolution are interdependent processes which basically follow the same logic. These considerations and results offer an explanation for the unique evolutionary path of Western civilization.