This text discusses the mathematical analysis of social systems, understood in the following way: social systems consist of social actors who interact according to specific rules of interactions; the dynamics of social systems is then the consequences of these interactions, viz., the self-organization of social systems. According to particular demands of their environment, social systems are able to behave in an adaptive manner, that is they can change their rules of interaction by certain meta rules and thus generate a meta dynamics. It is possible to model and analyze mathematically both dynamics and meta dynamics, using cellular automata and genetic algorithms. These tools allow social systems theory to be carried through as precisely as the theories of natural systems, a feat that has not previously been possible. The text should be of use to researchers and graduate students in the fields of theoretical sociology and social and general systems theory and other interested scientists.
