  The evolution of probability distribution functions (PDFs) of continuous
density, velocity and velocity derivatives ( deformation tensor) fields in the
theory of cosmological gravitational instability are considered. We show that
in the Newtonian theory the dynamical equations cannot be reduced to the closed
set of Lagrangian equations.
  Since continuous fields from galaxy surveys need sufficiently large smoothing
which exceeds the scale of nonlinearity, one can use the Zel'dovich
approximation to describe the mildly non-linear matter evolution, which allows
the closed set of Lagrangian equations. The closed kinetic equation for the
joint PDF of cosmological continuous fields is derived in this approximation.
  The analytical theory of the cosmological PDFs with arbitrary (including
Gaussian) initial statistics is developed, based on the solution on the kinetic
equaiton. For Gaussian initial fluctuations, the PDFs are parametrized by only
linear {\it rms} fluctuations $\sigma$ on given filtering scale. Density PDF
$P(\rho, t)$ and PDF $M(\lambda_1, \lambda_2, \lambda_3; t)$ of eigenvalues of
the deformation tensor field in the Eulerian space evolve very rapidly in
non-linear regime. On the contrary, velocity PDF $Q(\vec v, t)$ remains
invariant under non-linear evolution. For small $\sigma$ the Edgworth series is
suggested to reconstruct
