  These lectures notes give an introduction to the fast developing area of
research dealing with perturbative descriptions of the gravitational
instability in an expanding universe. I just sketch the outlines of some
proofs, and many important contributions (and references) were left out. Many
untouched aspects are reviewed in \cite{sah_col} which also contains a useful
reference list. In the notes dedicated to the Eulerian approach
(\S\ref{sec:fluid} - \S\ref{sec:further}), I derive the fluid equations
starting from a microscopic description, I give their linear solution and some
higher order corrections, and describe a number of applications concerning the
evolution of the one point probability density function for the density
contrast field and for the divergence of the corresponding velocity field. In
the notes dedicated to the Lagrangian point of view (\S\ref{sec:zeldo} -
\S\ref{sec:lag_app}), I recall Zeldovich Approximation and its higher orders
corrections, and present some applications, like their use in describing the
statistical effect of the real space-redshift mapping, or as approximate
description of the full non-linear dynamics.
