  The clustering in redshift space is studied here to first order within the
framework of gravitational instability. The distortion introduced by the
peculiar velocities of galaxies results in anisotropy in the galaxy
distribution and mode-mode coupling when analyzed in Fourier space. An exact
linear calculation of the full covariance matrix in both the real and Fourier
space is presented here. The explicit dependence on $\Omeg$ and the biasing
parameter is calculated and its potential use as a probe of these parameters is
analyzed. It is shown that Kaiser's formalism can be applied only to a data set
that subtends a small solid angle on the sky, and therefore cannot be used in
the case of all sky surveys. The covariance matrix in the real space is
calculated explicitly for {\it CDM} model, where the behavior along and
perpendicular to the line of sight is shown.
