We present results for Ly \alpha forest and metal absorbers from \sim 7 km s ^ { -1 } resolution data from the Space Telescope Imaging Spectrograph for the QSO PKS 0405–123 ( z = 0.574 , V = 14.9 ) . We analyze two samples of low redshift Ly \alpha forest lines , a sample of strong Ly \alpha lines and a sample of weak ones . The strong-line sample consists of 60 Ly \alpha absorbers detected at 4.0 \sigma significance with column density \log \mbox { $N _ { HI } $ } \geq 13.3 over 0.002 < z < 0.423 ; the sample of weak lines contains 44 absorbers with a column density limit of \log \mbox { $N _ { HI } $ } \geq 13.1 over 0.020 < z < 0.234 . Seven of the Ly \alpha absorbers show metal absorption lines . Notably , all of these metal systems appear to have associated O vi absorption , but the O vi is often offset in velocity from the Ly \alpha lines . We do not distinguish between metal and Ly \alpha -only systems in the following analysis , and use simulated spectra to aid in the interpretation of results . The Doppler parameter distribution for the strong sample has \langle b \rangle = 47 \pm 22 km s ^ { -1 } . For the weak sample , \langle b \rangle = 44 \pm 21 km s ^ { -1 } . Line blending and signal-to-noise effects likely inflate the Doppler parameters . The redshift density is consistent with previous , lower resolution measurements for \log \mbox { $N _ { HI } $ } \geq 14.0 . For absorbers with 13.1 < \log \mbox { $N _ { HI } $ } < 14.0 , we find results consistent with previous high resolution studies for z < 0.127 but an overdensity of \sim 0.2 - 0.3 dex at 0.127 < z < 0.234 , which we believe arises from cosmic variance . We find Ly \alpha -Ly \alpha clustering in our sample on a scale of \Delta v \leq 250 km s ^ { -1 } for \log \mbox { $N _ { HI } $ } \geq 13.3 , which is consistent in strength and velocity scale with a numerical model of structure evolution . There is a void in the strong absorber sample at 0.0320 < z < 0.0814 with probability of occurrence from a random redshift distribution of P < 0.0004 . We detect line-of-sight velocity correlations of up to 250 km s ^ { -1 } between Ly \alpha absorbers and 39 galaxies at z < 0.43 in the field out to transverse distances covering up to 1.6 h ^ { -1 } _ { 70 } Mpc in the local frame . The Ly \alpha -galaxy two point correlation function is significant out to \Delta v < 250 km s ^ { -1 } and grows with minimum absorber H i column density , with the strongest signal for \log \mbox { $N _ { HI } $ } { \gtrsim } 13.5 - 14.0 absorbers . The strength is similar to that of the galaxy-galaxy correlation for galaxies of the same mean luminosity as our sample , which implies that such Ly \alpha absorbers have masses \log M / M _ { \odot } = 11.3 ^ { +1.0 } _ { -0.6 } . The correlation becomes insignificant for a sample limited to 13.1 \leq \log \mbox { $N _ { HI } $ } < 14.3 . Including lower column density systems in the sample shows correlations only out to \Delta v < 125 km s ^ { -1 } , as would be expected for smaller density perturbations . 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 ^ { -1 } and the probability of occurrence from uncorrelated data of P = 0.0009 . Based on galaxy counts in the field , we predict regions of low H i column density at z \approx 0.45 and high values at z \approx 0.43 and z \approx 0.51 toward PKS 0405–123 . Finally , we present column densities for a number of Galactic species .