  This paper derives the expressions of the multipole moments of an isolated
gravitating source with an accuracy corresponding to the second post-Newtonian
(2-PN) approximation of general relativity. The moments are obtained by a
procedure of matching of the external gravitational field of the source to the
inner field, and are found to be given by integrals extending over the
stress-energy distribution of the matter fields and the gravitational field.
Although this is not manifest on their expressions, the moments have a compact
support limited to the material source only (they are thus perfectly
well-defined mathematically). From the multipole moments we deduce the
expressions of the asymptotic gravitational waveform and associated energy
generated by the source at the 2-PN approximation. This work, together with a
forthcoming work devoted to the application to coalescing compact binaries,
will be used in the future observations of gravitational radiation by laser
interferometric detectors.
