We examine the clustering properties of low-redshift Lya and heavy-element QSO absorption line systems seen in the spectra of 13 QSOs at the Galactic poles. This is the densest sample of D1i separat- ed QSOs observed spectroscopically with the Hubble Space Telescope to date. At the median redshift of the Lya sample (z B 0.7), the QSO lines of sight are separated on transverse scales from about 15 to 200 h~1 Mpc H 100 h km s~1 Mpc~1), allowing the three-dimensional clustering of the (q 0 0.5, absorbers to be examined on those scales. The Galactic poles are also regions where relatively deep and wide-—eld galaxy redshift surveys have taken place, so the distributions of galaxies and Lya systems can be compared within the same volume of space. There are 545 total absorption lines detected in the com- plete sample from 13 QSOs. We identify 307 Lya systems, of which 18 contain heavy-element lines. We con—rm the relatively slow redshift number density evolution for Lya systems at There are also z ( 1. —ve likely C IV doublets in our sample, for which the Lya line is not accessible. The main results are summarized as follows: 1. Most, but not all, of the very low-z (z 0.2) Lya systems appear to be associated with large-scale structures traced by luminous galaxies, based upon the spectrum of the low-redshift QSO PG 1309)355. 2. On scales of 2.5 to 5 h~1 Mpc, the line-of-sight correlation function shows a positive and signi—cant clustering amplitude, for systems with rest equivalent width, W , exceeding 0.24 m los 0.95 ^ 0.28, Ae . Most of this signal can be accounted for by a small number of Lya ii clumps, ˇˇ which typically contain about —ve systems spanning D20 h~1 Mpc. There is qualitative evidence that the strength of the corre- lation function rises with the limiting Lya rest equivalent width. 3. Over half of the heavy-element systems are either in groups or have a nearby ii clump ˇˇ of Lya lines. However, there is only weak evidence for a signi—cant heavy-element/Lya cross-correlation function. 4. There is no clear evidence that the Lya systems are distributed in redshift ii peaks ˇˇ and ii voids ˇˇ as is characteristic for the galaxies. In particular, there is no signi—cant periodicity detected on the scale of 128 h~1 Mpc, which had been detected for the galaxies located in the same direction of the sky. There is marginal evidence for a 41.5 h~1 Mpc ii periodicity ˇˇ in the distribution, which is seen for all equivalent width-limited samples. 5. The three-dimensional Lya radial correlation function shows no signi—cant departures from a random sample at any scale or using any limiting equivalent width. This indicates that if there are sheet- like structures spanning separations on the order of 30 h~1 Mpc or more, they are not clearly traced by Lya systems. 6. The fraction of Lya lines with W ( 0.24 which may be clustered in the same way as the heavy- Ae , element systems detected mostly at higher redshifts, is about 39% ^ 6%. This value is likely to depend on the limiting equivalent width and redshift of the sample. These results are consistent with a picture of the Lya forest at low redshift in which some fraction of the Lya lines arise in close proximity to galaxies and structures traced by galaxies, but in which a substantial fraction of the systems are also more uniformly distributed and are largely unrelated to the distribution of luminous galaxies. The results also appear to be in broad agreement with numerical simulations of the