  We study the relation between topological string theory and singularity
theory using the partition function of $A_{N-1}$ topological string defined by
matrix integral of Kontsevich type. Genus expansion of the free energy is
considered, and the genus $g=0$ contribution is shown to be described by a
special solution of $N$-reduced dispersionless KP system. We show a universal
correspondences between the time variables of dispersionless KP hierarchy and
the flat coordinates associated with versal deformations of simple
singularities of type $A$. We also study the behavior of topological matter
theory on the sphere in a topological gravity background, to clarify the role
of the topological string in the singularity theory. Finally we make some
comment on gravitational phase transition.
