  We present a new optical spectroscopic survey of 1777 'star-forming' ('SF')
and 366 'non-star-forming' ('non-SF') galaxies at redshifts z < 1 (2143 in
total), 22 AGN and 423 stars, observed by instruments such as DEIMOS, VIMOS and
GMOS, in 3 fields containing 5 quasi-stellar objects (QSOs) with HST UV
spectroscopy. We also present a new spectroscopic survey of 165 'strong' (10^14
< NHI < 10^17 cm^-2), and 489 'weak' (10^13 < NHI < 10^14 cm^-2) intervening HI
absorption line systems at z < 1 (654 in total), observed in the spectra of 8
QSOs by COS and FOS on the HST. Combining these new data with previously
published galaxy catalogs such as VVDS and GDDS, we have gathered a sample of
654 HI absorption systems and 17509 galaxies at transverse scales < 50 Mpc. We
present observational results on the HI-galaxy and galaxy-galaxy correlations
at transverse scales r < 10 Mpc, and the HI-HI auto-correlation at transverse
scales r < 2 Mpc. The two-point correlation functions are measured both along
and transverse to the line-of-sight. We constrain the HI-galaxy statistical
connection, as a function of both HI column density and galaxy star-forming
activity. Our results are consistent with the following conclusions: (1) the
bulk of HI systems on Mpc scales have little velocity dispersion (<120 km/s)
with respect to the bulk of galaxies; (2) the vast majority of strong HI
systems and SF galaxies are distributed in the same locations, together with
75+-15% of non-SF galaxies, all of which typically reside in dark matter haloes
of similar masses; (3) 25+-15% of non-SF galaxies reside in galaxy clusters and
are not correlated with strong HI systems at scales < 2 Mpc; and (4) 50% of
weak HI systems reside within galaxy voids (hence not correlated with
galaxies), and are confined in dark matter haloes of masses smaller than those
hosting... [abridged]
