  The cooling cores of clusters of galaxies are among the brightest thermal
X-ray line sources in the universe. High resolution X-ray spectra would allow
individual line fluxes to be measured. The fluxes of low ionization X-ray lines
in cooling flows should be directly proportional to the cooling rate at
relatively cool temperatures, and could be used to determine whether large
amounts of gas are really cooling out of the X-ray band (below 10e6 K). By
comparing the fluxes of many X-ray lines, we could determine the amounts of gas
at different temperatures and densities. This would allow one to test the idea
that cooling flows are highly inhomogeneous, as required to explain their
surface brightness profiles. High resolution X-ray spectra can be used to
determine velocities in the hot gas in cooling flows. If the gas is
homogeneous, significant inflow velocities are expected. However, if the gas is
as inhomogeneous as we currently believe, the inflow velocities are likely to
be rather low (v < 30 km/s). Most of the central galaxies in cooling flows host
radio sources, and it appears that the radio lobes are expanding against,
displacing, and compressing the cooling X-ray gas. Significant motions
associated with the expansion of radio sources should be detectable in X-ray
lines. If the cooling X-ray gas rotates and viscosity is not important,
rotational motions may also be detectable in X-ray line spectra.
