  We review the high resolution X-ray spectroscopy capabilities of the AXAF
observatory focusing on the High Energy Transmission Grating (HETG). As part of
the Guaranteed Time Observation (GTO) program, the HETG science team will
observe both elliptical galaxies and clusters of galaxies. We discuss the
problems associated with observing extended sources with the HETG and some of
the potential scientific insights which AXAF's spectroscopy capabilities can
provide for these classes of objects.
