  Based on the dispersionless KP (dKP) theory, we give a comprehensive study of
the topological Landau-Ginzburg (LG) theory characterized by a rational
potential. Writing the dKP hierarchy in a general form, we find that the
hierarchy naturally includes the dispersionless (continuous) limit of Toda
hierarchy and its generalizations having finite number of primaries. Several
flat solutions of the topological LG theory are obtained in this formulation,
and are identified with those discussed by Dubrovin. We explicitly construct
gravitational descendants for all the primary fields. Giving a residue formula
for the 3-point functions of the fields, we show that these 3-point functions
satisfy the topological recursion relation. The string equation is obtained as
the generalized hodograph solutions of the dKP hierarchy, which show that all
the gravitational effects to the constitutive equations (2-point functions) can
be renormalized into the coupling constants in the small phase space.
