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How and when galaxies formed are questions at the forefront of work in observational cosmology. While the baryonic content of galaxies observed in the present epoch is concentrated in stars, in the past this must have been in the form of gas. Damped \lya absorption systems (N(HI)$\ge 2 \times 10^{20}$cm$^{-2}$) dominate the baryonic mass contributed by HI. The APM Damped \lya Survey (Storrie-Lombardi et~al., 1995) identified fourteen candidate systems in the redshift range $2.8\le z \le 4.4$ (11 with $z>3.5$). These data more than triple the redshift path surveyed at z$>$3 and allow the first systematic study up to z=4.5. Combining the APM data with previous surveys we find evidence for a turnover at z$\sim$3 or a flattening at z$\sim$2 in the cosmological mass density of neutral gas, $\Omega_g$. The shape of the $\Omega_g$ curve has profound implications for galaxy formation theories. A fall-off in the curve with increasing redshift points to an epoch where the damped \lya systems are still collapsing. A program of followup spectroscopy of the candidate damped \lya absorbers from the APM survey has been been undertaken at Keck with LRIS to confirm the candidate systems and obtain accurate column densities (Storrie-Lombardi \& Wolfe 1995). Initial results will be presented.
