  In these lecture notes we discuss a body of work in which Morse theory is
used to construct various homology and cohomology operations. In the classical
setting of algebraic topology this is done by constructing a moduli space of
graph flows, using homotopy theoretic methods to construct a virtual
fundamental class, and evaluating cohomology classes on this fundamental class.
By using similar constructions based on "fat" or ribbon graphs, we describe how
to construct string topology operations on the loop space of a manifold, using
Morse theoretic techniques. Finally, we discuss how to relate these string
topology operations to the counting of J - holomorphic curves in the cotangent
bundle. We end with speculations about the relationship between the absolute
and relative Gromov-Witten theory of the cotangent bundle, and the open-closed
string topology of the underlying manifold.
