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The formation of galaxies is studied in the context of the fragmentation of massive diffuse ionized gas clouds. A semiquantitative discussion of the role of cooling indicates that there is a characteristic mass of a galaxy (of the order of 500 billion solar masses) which can fragment out of an ionized medium of density not exceeding 10 to the-25th power g/cu cm, whereas more massive galaxies attain a characteristic radius of the order of 60 kpc. The relationship between binding energy and mass is investigated for spheroidal galaxies. The role of H2 and Ly-alpha cooling in the fragmentation of primordial gas clouds is evaluated, and relatively qualitative arguments indicate that the first stars have masses of at least 0.3 solar mass with a characteristic mass of approximately 20 solar masses. When the average heavy-element abundance by mass exceeds about 0.00001, heavy-element cooling prevails over Ly-alpha …