  Old and new puzzles of cosmology are reexamined from the point of view of
quantum theory of the universe developed here. It is shown that in proposed
approach the difficulties of the standard cosmology do not arise. The theory
predicts the observed dimensions of the nonhomogeneities of matter density and
the amplitude of the fluctuations of the cosmic background radiation
temperature in the Universe and points to a new quantum mechanism of their
origin. It allows to obtain the value of the deceleration parameter which is in
good agreement with the recent SNe Ia measurements. The theory explains the
large value of entropy of the Universe and describes other parameters.
