We present initial results of a program to obtain and analyze HST WFPC2 images of galaxies identified in an imaging and spectroscopic survey of faint galaxies in fields of HST spectroscopic target QSOs . We measure properties of 87 galaxies , of which 33 are associated with corresponding { Ly } \alpha absorption systems and 24 do not produce corresponding { Ly } \alpha absorption lines to within sensitive upper limits . Considering only galaxy and absorber pairs that are likely to be physically associated and excluding galaxy and absorber pairs within 3000 km s { { } ^ { -1 } } of the background QSOs leaves 26 galaxy and absorber pairs and seven galaxies that do not produce corresponding { Ly } \alpha absorption lines to within sensitive upper limits . Redshifts of the galaxy and absorber pairs range from 0.0750 to 0.8912 with a median of 0.3718 , and impact parameter separations of the galaxy and absorber pairs range from 12.4 to 157.4 h ^ { -1 } kpc with a median of 62.4 h ^ { -1 } kpc . The primary result of the analysis is that the amount of gas encountered along the line of sight depends on the galaxy impact parameter and B -band luminosity but does not depend strongly on the galaxy average surface brightness , disk-to-bulge ratio , or redshift . This result confirms and improves upon the anti-correlation between { Ly } \alpha absorption equivalent width and galaxy impact parameter found previously by Lanzetta et al . ( 1995 ) . Spherical halos can not be distinguished from flattened disks on the basis of the current observations , and there is no evidence that galaxy interactions play an important role in distributing tenuous gas around galaxies in most cases . Galaxies might account for all { Ly } \alpha absorption systems with W > 0.3 Å , but this depends on the unknown luminosity function and gaseous cross sections of low-luminosity galaxies as well as on the uncertainties of the observed number density of { Ly } \alpha absorption systems .