  This paper constructs the multipole expansion (in general relativity) of the
gravitational field generated by a slowly-moving isolated source. We introduce
some definitions for the source multipole moments, valid to all orders in a
post-Newtonian expansion, and depending in a well-defined way on the total
stress-energy pseudo-tensor of the material and gravitational fields.
Previously obtained expressions of the source multipole moments are recovered
in the appropriate limits. The source moments parametrize the linearized
approximation of the gravitational field exterior to the source, as computed by
means of a specific post-Minkowskian algorithm defined in a previous work.
Since the radiative multipole moments parametrizing the radiation field far
from the source can be obtained as non-linear functionals of the source
moments, the present paper permits relating the radiation field far from a
slowly-moving source to the stress-energy pseudo-tensor of the source. This
should be useful when comparing to theory the future observations of
gravitational radiation by the LIGO and VIRGO experiments.
