  We present a coarse-grained field theory of density fluctuations for a
Newtonian self-gravitating many-body system and apply it to a homogeneous
Universe with small density fluctuations. The theory treats the clustering of
galaxies and clusters in terms of the field of density fluctuations. The Jeans
length $\lambda_0$, a unique physical scale for a gravitating system, appears
naturally as the characteristic scale underlying the large scale structure.
Under Gaussian approximation the analytic expressions of $\xi(r)$ and $P(k)$
are obtained. The correlation amplitude is proportional to the galactic mass,
and is oscillating over large scales $\sim 100$ $h^{-1}$ Mpc and damped to
zero. The spectrum amplitude is inversely proportional to the galactic number
density.The preliminary results qualitatively explain some pronounced features
of large scale structures.
