We develop an analytical core for sociology. We follow standard dynamical systems theory by first specifying the conditions for social equilibrium, and then studying the dynamical principles that govern disequilibrium behavior. Our general social equilibrium model is an expansion of the general equilibrium model of economic theory, and our dynamical principles treat the society as a complex adaptive system that can be studied using evolutionary game theory and agent-based Markov models based on variants of the replicator dynamic.