  We discuss various analytical approximation methods for the evolution of the
density fluctuation in the Universe. From primordial density fluctuation, the
large-scale structure is formed via its own self-gravitational instability. For
this dynamical evolution, several approaches have been considered. In Newtonian
cosmology, in which matter motion is described by Newtonian dynamics with
cosmic expansion, Lagrangian description for the cosmic fluid is known to work
rather well for quasi-nonlinear clustering regime. In this paper, we briefly
review Lagrangian perturbation theory in Newtonian cosmology.
