  We present results of our HST Cycle 11 Survey for low-redshift (z<1.65) DLAs
in the UV spectra of quasars selected from the SDSS Early Data Release. These
quasars have strong intervening MgII-FeII systems which are known signatures of
high column density neutral gas. In total, UV observations of Ly-alpha
absorption in 197 MgII systems with z<1.65 and rest equivalent width (REW)
W2796 \ge 0.3A have now been obtained. The main results are: (1) 36(+/- 6)% of
systems with W2796 \ge 0.5 A and FeII W2600 \ge 0.5 A are DLAs. This increases
to 42(+/- 7)% for systems with W2796/W2600 < 2 and MgI W2852 > 0.1 A. (2) The
mean N(HI) of MgII systems with 0.3 A \le W2796 < 0.6 A is a factor of ~36
lower than that of systems with W2796 \ge 0.6 A. (3) The DLA incidence per unit
redshift is consistent with no evolution for z <~ 2 (Omega_L=0.7, Omega_M =
0.3), but exhibits significant evolution for z >~ 2. (4) Omega_{DLA} is
constant for 0.5<z<5.0 to within the uncertainties. This is larger than
Omega_{gas}(z=0) by a factor of ~2. (5) The slope of the N(HI) distribution
does not change significantly with redshift. However, the low redshift
distribution is marginally flatter due to the higher fraction of high N(HI)
systems in our sample. (6) Finally, using the precision of MgII survey
statistics, we find that there may be evidence of a decreasing Omega_{DLA} from
z=0.5 to z=0. We reiterate the conclusion of Hopkins, Rao, & Turnshek that very
high columns of neutral gas might be missed by DLA surveys because of their
very small cross sections, and therefore, that Omega_{DLA} might not include
the bulk of the neutral gas mass in the Universe. (Abridged)
