The low-redshift Lyα 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 Lyα clouds toward nearby Seyferts and QSOs, including their frequency, space density, estimated mass, association with galaxies, and contribution to Ωb. Our HST/GHRS detections of ∼ 70 Lyα absorbers with N hi ≥ 1012·6 cm−2 along 11 sightlines covering pathlength Δ(cz) = 114,000 km s−1 show f (>N hi ) α N hi −0·63±0·04 and a line frequency dN/dz = 200 ± 40 for N hi > 1012·6 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) kpc from four large galaxies, with low metallicity (≤0·003 solar) and D/H ≤ 2 × 10−4. At low-z, we derive a metagalactic ionising radiation field from AGN of J 0 = × 10−23 erg cm−2 s−1 Hz−1 sr−1 and a Lyα-forest baryon density Ωb =(0·008 ± 0·004)[J −23 N 14 b 100]½ for clouds of characteristic size b = (100 kpc)b 100.