We derive the statistical properties of neutral gas at redshifts 0.11<z<1.65 from UV measurements of quasar Lyman alpha absorption lines corresponding to 369 MgII systems with $W^{\lambda2796}_{0} \ge 0.3$ \AA. In addition to the 41 damped Lyman alpha (DLA) systems presented in Rao et al. (2006), the current DLA sample includes 29 newly discovered DLAs. Of these, 26 were found in our HST ACS prism survey for DLAs (Turnshek et al. 2015) and three were found in a GALEX archival search. In addition, an HST COS Cycle 19 survey yielded no DLAs that could be used for this study. Formally, this DLA sample includes 70 systems with $N_{\rm HI}\ge 2\times 10^{20}$ atoms cm$^{-2}$. We find that the incidence of DLAs, or the product of their gas cross section and their comoving number density, can be described by $n_{\rm DLA}(z) = (0.027 \pm 0.007) (1+z)^{(1.682 \pm 0.200)}$ over the redshift range 0<z<5. The cosmic mass density of neutral gas can be described by $\Omega_{\rm DLA}(z) = (4.77 \pm 1.60)\times10^{-4} (1 + z)^{(0.64\pm 0.27)}$. The low-redshift column density distribution function is well-fitted by a power law of the form $f(N) \sim N^\beta$ with $\beta = -1.46 \pm 0.20$. It is consistent with the high-redshift as well as z=0 estimates at the high column density end but, lies between them at the low column density end. We discuss possible $N_{\rm HI}$ and metallicity bias in MgII-selected DLA samples and show that such biases do not exist in the current data at z<1.65. Thus, at least at z<1.65, DLAs found through MgII selection statistically represent the true population of DLAs. However, we caution that studies of DLA metallicities should take into the account the relative incidence of DLAs with respect to $W^{\lambda2796}_{0}$ (or gas velocity spread) in order to correctly measure the mean neutral-gas cosmic metallicity of the universe.