  This paper reviews the essential physics of gravitational instability in a
Robertson-Walker background spacetime. Three approaches are presented in a
pedagogical manner, based on (1) the Eulerian fluid equations, (2) the
Lagrangian description of trajectories, and (3) the Lagrangian fluid equations.
Linear and nonlinear limits are discussed for each case. Shear and tides are
shown to play a key role in nonlinear gravitational instability.
  The Lagrangian fluid approach is used to show that several widely held
beliefs about gravitational instability are false. The following collapse
theorem is proven: for a given initial density fluctuation and growth rate, the
spherical tophat perturbation collapses more slowly than any other
configuration. We also show that density maxima are not the first points to
collapse and that underdense regions may collapse if their initial shear is
sufficiently high. The Lagrangian fluid approach leads to an almost closed set
of local evolution equations for individual mass elements. The magnetic part of
the Weyl tensor, which may be present even in the nonrelativistic (Newtonian)
limit, may prevent a purely local description. However, neglecting the magnetic
part of the Weyl tensor, we obtain predictions for high-redshift collapse that
are in good agreement with a high-resolution cold dark matter N-body
simulation.

Astrophysics