  A systematic formulation of the higher genus expansion in topological string
theory is considered. We also develop a simple way of evaluating genus zero
correlation functions. At higher genera we derive some interesting formulas for
the free energy in the $A_1$ and $A_2$ models. We present some evidence that
topological minimal models associated with Lie algebras other than the A-D-E
type do not have a consistent higher genus expansion beyond genus one. We also
present some new results on the $CP^1$ model at higher genera.
