  Dynamical systems theory is especially well-suited for determining the
possible asymptotic states (at both early and late times) of cosmological
models, particularly when the governing equations are a finite system of
autonomous ordinary differential equations. We begin with a brief review of
dynamical systems theory. We then discuss cosmological models as dynamical
systems and point out the important role of self-similar models. We review the
asymptotic properties of spatially homogeneous perfect fluid models in general
relativity. We then discuss some results concerning scalar field models with an
exponential potential (both with and without barotropic matter). Finally, we
discuss some isotropic cosmological models derived from the string effective
action.
