  We describe our surveys of low column density Lyman-alpha absorbers [N(HI) =
10^(12.5-16.0) cm^-2], which show that the warm photoionized IGM contains 30%
of all baryons at z < 0.1. This fraction is consistent with cosmological
simulations, which also predict that an additional 20-40% of the baryons reside
in hotter 10^(5-7) K gas, the warm-hot IGM (WHIM). The observed line density of
Lya absorbers, dN/dz = 170 for N(HI) > 10^(12.8) cm^-2, is dominated by
low-N(HI) systems that exhibit slower redshift evolution than those with N(HI)
>10^(14). HST/FUSE surveys of OVI absorbers, together with recent detections of
O VII with Chandra and XMM/Newton, suggest that 20-70% of all baryons could
reside in the WHIM, depending on its assumed abundance (O/H = 10% solar). At
the highest column densities, N(HI) > 10^(20.3), the damped Lya systems are
often identified with gas-rich disks of galaxies over a large range in
luminosities (0.03-1 L*) and morphologies. Lyman-limit systems [N(HI) =
10^(17.3-20.3)] appear to be associated with bound, bright (0.1-0.3 L*) galaxy
halos. The Lya absorbers with N(HI) = 10^(13-16) cm^-2 are associated with
filaments of large-scale structure in the galaxy distribution, although some
may arise in unbound winds from dwarf galaxies. Our discovery that ~20% of
low-z Lya absorbers reside in galaxy voids suggests that a substantial fraction
of baryons may be entirely unrelated to galaxies. In the future, Hubble (and
FUSE) can provide a census of the local baryons and the distribution of heavy
elements in the IGM. These studies can be conducted quite efficiently if NASA
can install the Cosmic Origins Spectrograph (COS) on Hubble, allowing an
order-of-magnitude improvement in throughput and a comparable increase in our
ability to study the IGM.
