  The main results for the two-dimensional quantum gravity, conjectured from
the matrix model or integrable approach, are presented in the form to be
compared with the world-sheet or Liouville approach. In spherical limit the
integrable side for minimal string theories is completely formulated using
simple manipulations with two polynomials, based on residue formulas from
quasiclassical hierarchies. Explicit computations for particular models are
performed and certain delicate issues of nontrivial relations among them are
discussed. They concern the connections between different theories, obtained as
expansions of basically the same stringy solution to dispersionless KP
hierarchy in different backgrounds, characterized by nonvanishing background
values of different times, being the simplest known example of change of the
quantum numbers of physical observables, when moving to a different point in
the moduli space of the theory.
