  A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in
the presence of 1-component perfect-fluid and minimally coupled scalar field is
considered. When the pressures in all spaces are proportional to the density,
the Einstein and Wheeler-DeWitt equations are integrated for a large variety of
parameters. Classical and quantum wormhole solutions are obtained for negative
density. Some special classes of solutions, e.g. solutions with spontaneous and
dynamical compactification, exponential and power-law inflations, are singled
out. For positive density a third quantized cosmological model is considered
and the Planckian spectrum of ``created universes'' is obtained.
