  Inspiralling binary systems of neutron stars or black holes are promising
sources of gravitational radiation detectable by large-scale laser
interferometric gravitational observatories, such as the US LIGO and
Italian-French VIRGO projects. Accurate theoretical gravitational-waveform
templates will be needed to carry out matched filtering data analysis of the
detectors' output once they are on the air by the end of this decade. For all
but the final, strongly general relativistic coalescence of the two bodies,
high-order post-Newtonian methods are playing a major role in the theorists'
efforts to develop the needed templates. This paper discusses the foundations
of this method, and provides a compendium of useful formulae and results.
Figures available upon request. (Invited talk given at the 8th
Nishinomiya-Yukawa Memorial Symposium, October 28, 1993.)
