We present results from an efficient, nontraditional survey to discover damped Lya (DLA) absorption systems with neutral hydrogen column densities atoms cm~2 and redshifts z \ 1.65. In N H I º 2 ] 1020 the past, identiÐcation of DLA systems at z \ 1.65 has been difficult because of their rare incidence and the need for UV spectroscopy to detect Lya absorption at these low redshifts. Our survey relies on the fact that all known DLA systems have corresponding Mg II absorption. In turn, Mg II absorption systems have been well studied, and their incidence at redshifts 0.1 \ z \ 2.2 as a function of the Mg II rest equivalent width, is known. Therefore, by observing the Lya line corresponding to identiÐed W 0 j2796, low-redshift Mg II systems and determining the fraction of these that are damped, we have been able to infer the statistical properties of the low-redshift DLA population. In an earlier (1995) paper we presented initial results from an archival study with data from the Hubble Space T elescope (HST ) and IUE. Now, with new data from our HST GO program, we have more than doubled the sample of Mg II systems with available ultraviolet spectroscopic data. In total we have uncovered 12 DLA lines in 87 Mg II systems with Two more DLA systems were discovered serendipitously in our W 0 j2796 º 0.3 A . HST spectra. At the present time the total number of conÐrmed DLA systems at redshifts z \ 1.65 is 23.The signiÐcant results of the survey are as follows. (1) The DLA absorbers are drawn almost exclusively from the population of Mg II absorbers that have Moreover, half of all absorp-W 0 j2796 º 0.6 A . tion systems with both Mg II and Fe II are DLA systems. (2) The incidence of W 0 j2796 W 0 j2600 [ 0.5 A DLA systems per unit redshift, decreases as a function of decreasing redshift. The low-redshift data n DLA , are consistent with the larger incidence of DLA systems seen at high redshift and the inferred low incidence for DLA at z \ 0 derived from 21 cm observations of gas-rich spirals. However, the errors in our determination are large enough that it is not clear if the decrease per comoving volume begins to be signiÐcant at z B 2 or possibly does not set in until z B 0.5. (3) On the other hand, the cosmological mass density of neutral gas in low-redshift DLA absorbers, is observed to be comparable to that ) DLA , observed at high redshift. In particular, there is no observed trend that would indicate that at low ) DLA redshift is approaching the value at z \ 0, which is a factor of B4È6.5 lower than (4) The low-) DLA . redshift DLA absorbers exhibit a larger fraction of very high column density systems in comparison to determinations both at high redshift and at z \ 0. In addition, at no redshift is the column density distribution of DLA absorbers observed to fall o † in proportion to with increasing column density, DN H Ĩ 3 a trend that is theoretically predicted for disklike systems. We discuss this and other mounting evidence that DLA absorption arises not solely in luminous disks but in a mixture of gal...