  Topological quantum field theories containing matter fields are constructed
by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$
chiral (antichiral) multiplets lead to topological sigma models while $N=2$
twisted chiral (twisted antichiral) multiplets lead to Landau-Ginzburg type
topological quantum field theories. In addition, topological gravity in two
dimensions is formulated using a gauge principle applied to the topological
algebra which results after the twisting of $N=2$ supersymmetry.
