Molecular hydrogen in the high redshift damped Ly-α systems

This review talk summarizes the main results obtained from the just completed survey of molecular hydrogen in damped Lyman-alpha systems (DLAs). Preliminary results based on modeling ionization conditions and chemical network is also presented. The presence of H(2) and fine-structure lines of C I in 13-20% of DLAs allow one to investigate the physical conditions using the techniques that are commonly used in the studies of the Galactic ISM. It is shown that the DLAs with H(2) trace regions with higher density, lower temperature, moderate to high dust depletion, and local star-formation. Absence of H(2) in DLAs with moderate dust depletion could just be a simple consequence of lower densities in the systems.