In this preparatory talk, I will explain background that will be used in the topology seminar.  Those planning to attend that talk and not familar with the list of topics here should probably come to this one too.  Topics: Lyapunov exponents.  Connection to subexponential growth.  Lyapunov exponents as linear functionals for higher rank abelian group actions.  Ratner's theorem, averaging over unipotents (Shah's theorem) and the magic of entropy.