Theoretical models of galaxies consider their origin and evolution. It is difficult to review the early history of these theories and identify which of them have had a decisive influence on our present ideas. Most contemporary theories about the origin of galaxies are based on three decisive papers by Press and Schechter (1974), White and Rees (1978) and Peebles (1982), which will be commented on later, and have in common the hypothesis that the dark matter is cold (CDM) and that, at a given time, CDM halos arose through a hierarchy of different sized halos formed from mergers of smaller halos. At least four steps characterize the evolution of a galaxy:
a) Small density fluctuations, probably originated by quantum fluctuations before the epoch of Inflation or at cosmological phase transitions, grow during the radiation dominated universe and provide a fluctuation spectrum after the epoch of Recombination.
b) CDM overdensities accrete matter and merge. The hierarchical formation of greater and greater halos produces the present galactic and cluster structures.
c) Baryons cool and concentrate at the centre of halos and constitute the visible component of galaxies. The explanation of the Hubble sequence and the origin of rotation of galaxies would be goals of the study of this phase.
d) Once the basic structure of a galaxy with its different components has been established, it is necessary to follow its evolution due to star formation, gas ejected from stars, progressive metal enrichment, matter flows connecting the intra and extra media, small internal motions, etc.