  The aim of the present thesis is to review the Blanchet-Damour approach to
analytical study of gravitational waves emitted by localized perfect fluid
sources. It is assumed these perfect fluids are such that it is possible to
define small parameters for asymptotic expansions. Asymptotic expansions in
this approach are called post-Minkowskian and post-Newtonian expansions. By
plugging these expansions into the Einstein field equation, post-Minkowskian
and post-Newtonian equations are obtained. The usual methods for solving these
equations are to use the retarded and Poisson integrals. However, they cannot
provide solutions up to any arbitrary order in these cases because of their
divergence. In fact, these divergences motivated Blanchet and Damour to employ
a new approach to solve the post-Minkowskian and post-Newtonian equations. They
obtained the general solutions by means of a specific process of analytic
continuation. These solutions have some unknown terms that if one determines,
the gravitational field is described everywhere in $\mathbb{R}^3$. A matching
procedure, which depends deeply on analytic continuation, is used to determine
these unknown terms.
