We study the formation of molecular hydrogen, after the epoch of reionization, in the context of canonical galaxy formation theory due to hierarchical clustering. There is an initial epoch of H_2 production in the gas phase through the H~- route that ends at a redshift of order unity. We assume that the fundamental units in the gas phase of protogalaxies during this epoch are similar to diffuse clouds found in our own Galaxy, and we restrict our attention to protogalactic disks, although some of our analysis applies to multiphase halo gas. Giant molecular clouds are not formed until lower redshifts. Star formation in the protogalactic disks can become self-regulated. The process responsible for the feedback is the heating of the gas by the internal stellar radiation field that can dominate the background radiation field at various epochs. If the gas is heated to above 2000-3000 K, the hydrogen molecules are collisionally dissociated, and we assume that in their absence the star formation process is strongly suppressed because of insufficient cooling. As we demonstrate by the analysis of phase diagrams, the H_2-induced cool phase disappears. A priori, the cool phase with molecular hydrogen cooling can only achieve temperatures ≥ 300 K. Consequently, it is possible to define a maximum star formation rate during this epoch. Plausible estimates give a rate of approx < 0.2-2 solar mass yr~(-1) for condensations corresponding to 1σ and 2σ initial density fluctuations. For more massive structures, this limit is relaxed and in agreement with observations of high-redshift galaxies. Therefore, the production of metals and dust proceeds slowly in this phase. This moderate epoch is terminated by a phase transition to a cold, dense, and warm neutral/ionized medium once the metals and dust have increased to a level Z ≈ 0.03-0.1 Z_☉. Then (1) atoms and molecules such as C, O, and CO become abundant and cool the gas to below 300 K; (2) the dust abundance has become sufficiently high to allow shielding of the molecular gas; and (3) molecular hydrogen formation can occur rapidly on grain surfaces. This phase transition occurs at a redshift of approximately 1.5, with a fiducial range of 1.2 ≤ z ≤ 2, and initiates the rapid formation of molecular species, giant molecular clouds, and stars. Consequently, the delayed initiation of the cold phase in the interstellar medium of protostellar disks at a metallicity of Z approx < 0.1 Z_☉ is a plausible physical reason why the formation phase of the stellar disks of the bulk of the galaxies occurs only at a redshift of order unity. The combination of feedback and a phase transition provides a natural resolution of the G-dwarf problem.
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