We derive the statistical properties of neutral gas at redshifts 0.11<z<1.65 from ultraviolet (UV) measurements of quasar Ly{alpha} absorption lines corresponding to 369 MgII systems with W{lambda}2796_0_>=0.3{AA}. In addition to the 41 damped Lyman alpha (DLA) systems presented in Rao et al. (2006ApJ...636..610R, Cat. J/ApJ/636/610), the current DLA sample includes 29 newly discovered DLAs. Formally, this DLA sample includes 70 systems with N_HI_>=2*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_DLA_(z)=(0.027+/-0.007)(1+z)^(1.682+/-0.200)^ over the redshift range of 0<z<5. The cosmic mass density of neutral gas can be described by {Omega}_DLA_(z)=(4.77+/-1.60)x10^-4^(1+z)^(0.64+/-0.27)^. The low-redshift column density distribution function is well fitted by a power law of the form f(N)~N^{beta}^ with {beta}=-1.46+/-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_HI_ and metallicity bias in Mg II-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 account the relative incidence of DLAs with respect to W_0_{lambda}2796^ (or gas velocity spread) in order to