We present results for Ly forest and metal absorbers from $7 km s À1 resolution Space Telescope Imaging Spectrograph data for QSO PKS 0405À123 (z ¼ 0:574). We analyze strong and weak samples of Ly forest lines, containing 60 absorbers with column density log N H i ! 13:3 over 0:002 < z < 0:423 and 44 with log N H i ! 13:1 over 0:020 < z < 0:234, respectively. Seven absorbers contain metals, all with associated O vi and often offset in velocity from Ly. The strong and weak Doppler parameter distributions have hbi ¼ 47 AE 22 and 44 AE 21 km s À1 , respectively. Simulated spectra suggest that line blending and signal-to-noise ratio effects inflate b. For absorbers with 13:1 < log N H i < 14:0, we find a redshift overdensity of $0.2-0.3 dex at 0:127 < z < 0:234, which we attribute to cosmic variance. There is a void in the strong sample at 0:0320 < z < 0:0814 with probability of random occurrence P < 0:0004. We detect Ly-Ly clustering in our sample on a scale of Áv 250 km s À1 for log N H i ! 13:3, consistent with a numerical model of structure evolution. We detect velocity correlations of up to 250 km s À1 between Ly absorbers and 39 galaxies at z < 0:43 out to a transverse distance of 1.6 h À1 70 local frame Mpc. The Ly-galaxy two-point correlation function is significant out to Áv < 250 km s À1 and grows with minimum H i column density. The strongest signal occurs for log N H i k13:5 14:0 absorbers and is similar to the galaxy-galaxy correlation, implying that such Ly absorbers have masses log (M /M ) ¼ 11:3 þ1:0 À0:6 . We find a correlation between local galaxy counts and local summed H i column density, with peak significance on scales of 4000-6000 km s À1 and probability of random occurrence P ¼ 0:0009. Finally, we present column densities for a number of Galactic species.