  We set up a model for the evolution of the galaxy luminosity function, taking
advantage of recent work that brought in some better understanding of the mass
function for gravitationally condensed objects. The physics of cooling of the
baryonic component allows us to distinguish halos that become groups or
clusters from those that eventually form galaxies (possibly within the former
objects). With our new mass function and our new application of the cooling
criteria - which motivated this paper - we get a satisfactory and natural
cutoff at the bright end of the luminosity function, the needed flat slope for
faint magnitudes and the correct trend in colors (brighter galaxies are redder
) within the framework of the hierarchical clustering picture. This infirms
earlier claims that the latter was inadequate to reproduce the former
observations. We find the velocity dispersion to be a much better parameter
than mass or radius to characterize galaxies. We find that bright galaxies form
at z~2 from mergers with a rather quiet evolution afterwards, whereas small
galaxies are the result of a continuous merging process active up to the
present epoch. The transition is found to occur at the observed transition
between bright spirals and small dwarf ellipticals or irregulars. The quasar
multiplicity as a function of redshift is also discussed.
