Rich galaxy clusters are the largest dynamically relaxed systems in the universe, and as such provide some of the best available sites for studying the distribution of dark matter. Because of their high central densities, clusters are also useful as "laboratories" for studying the physics of galaxy-galaxy and galaxy-dark matter interactions. Over the last few years, as redshift surveys have begun to shed light on the distribution of galaxies on larger and larger scales, interest in the internal dynamics of galaxy clusters has declined. This is too bad, because new observational techniques have greatly increased the speed with which photometric and kinematical data on cluster galaxies can be obtained. Furthermore, there are a number of fundamental questions concerning the dynamics and evolution of galaxy clusters that remain to be convincingly answered. These questions include: What is the detailed distribution of dark matter in clusters? Is it more or less centrally concentrated than the galaxies? What fraction of the dark matter is bound to galaxies, i.e., do galaxies in clusters have massive dark halos? Do encounters between galaxies in clusters significantly affect their internal dynamics or their observable properties? Do galaxy orbits decay appreciably after cluster formation, and if so, is it possible to form a very bright "cD" galaxy through the repeated accretion of galaxies whose orbits have decayed?
This article will review our current understanding of the dynamics and post-collapse evolution of rich clusters. It will be assumed throughout that clusters may be usefully approximated as spherical, relaxed systems that are dynamically uncoupled from the surrounding universe. Such an assumption is dangerous, since much recent work suggests that subclustering and infall are common phenomena, and hence that many clusters are still in the throes of formation. Nevertheless a simple model may still be relevant for the inner regions of clusters where dynamcal times are much shorter than the age of the universe.
Because of the prominent role which it has played in observational and theoretical studies, the Coma cluster will be singled out for attention here, even though Coma may not be typical of the majority of rich clusters in terms of its richness or density (both of which are very high).