The low-redshift Ly \alpha forest of absorption lines provides a probe of large-scale baryonic structures in the intergalactic medium , some of which may be remnants of physical conditions set up during the epoch of galaxy formation . We discuss our recent Hubble Space Telescope ( HST ) observations and interpretation of low- z Ly \alpha clouds toward nearby Seyferts and QSOs , including their frequency , space density , estimated mass , association with galaxies , and contribution to \Omega _ { b } . Our HST/GHRS detections of \sim 70 Ly \alpha absorbers with N _ { HI } \geq 10 ^ { 12.6 } cm ^ { -2 } along 11 sightlines covering pathlength \Delta ( cz ) = 114 , 000 km s ^ { -1 } show f ( > N _ { HI } ) \propto N _ { HI } ^ { -0.63 \pm 0.04 } and a line frequency d { \cal N } / dz = 200 \pm 40 for N _ { HI } > 10 ^ { 12.6 } cm ^ { -2 } ( one every 1500 km s ^ { -1 } of redshift ) . A group of strong absorbers toward PKS 2155-304 may be associated with gas ( 400 - 800 ) h _ { 75 } ^ { -1 } kpc from 4 large galaxies , with low metallicity ( \leq 0.003 solar ) and D/H \leq 2 \times 10 ^ { -4 } . At low- z , we derive a metagalactic ionizing radiation field from AGN of J _ { 0 } = 1.3 ^ { +0.8 } _ { -0.5 } \times 10 ^ { -23 } ergs cm ^ { -2 } s ^ { -1 } Hz ^ { -1 } sr ^ { -1 } and a Ly \alpha -forest baryon density \Omega _ { b } = ( 0.008 \pm 0.004 ) h _ { 75 } ^ { -1 } [ J _ { -23 } N _ { 14 } b _ { 100 } ] ^ { 1 / 2 } for clouds of characteristic size b = ( 100 ~ { } { kpc } ) b _ { 100 } .