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The study of galaxies is not anymore only a "taxonomical" task. We are arriving now at a "genetical" level of their understanding, which opens the possibility to explain their diversity, in particular the origin of the HS. A relevant question emerges: is the origin of the HS dominated by cosmological conditions (nature) or by ulterior astrophysical processes (nurture)? The inductive approach has been particularly useful for exploring the latter item. A key aspect is the identification and the interconnection of the astrophysical processes that drive changes in the Hubble type, as well as the identification of observable fossil records of the different evolutionary phases. Models of spectrophotometric, chemical and dynamical evolution are the instruments which helped to reconstruct the past history from the observed fossil records. Most of the results from studies related to the inductive approach showed the necessity to connect galaxy evolution to external conditions. These conditions can be given by a cosmological scenario of structure formation.

The success of the inflationary CDM cosmology has pushed researchers to explore their ultimate consequences regarding galaxy formation (deductive approach). The predictions of models and simulations are encouraging; the hierarchical CDM model offers an invaluable theoretical background for understanding galaxies. The formation and evolution of disk galaxies within the CDM halos (Section 2) has been modeled with a minimum of free astrophysical parameters (Section 4). Therefore, the confrontation between theory and observations is particularly promising in this case. It seems that most of the properties and correlations of disk galaxies, including the correlations along the HS, are strongly linked to the initial conditions of the hierarchical CDM cosmology. A potential problem of the inside-out disks is their rapid size evolution, which could not be confirmed by high-redshift observations. More detailed comparisons of models and observations are needed at all the levels. They will allow to trace some properties of the early universe, as well as to infer the nature of the mysterious dark matter. As a result of some of these comparisons, galaxy-sized CDM halos seem to be too cuspy and with too much substructure. If the dark particles are assumed with some self-interacting properties or warm instead of cold, then the agreement with observations improves (Section 2).

The situation concerning spheroids is more complex than for disks. The age of the isolated spheroids and the details of the disk growing around the bulges are among the issues which keep open the debate about the congruency of the hierarchical cosmogony regarding spheroid formation. While the backbone of spheroid formation might be again the dark matter processes (major mergers mainly), complex astrophysical processes (e.g., non-stationary SF, strong feedback and cooling, dynamical processes, angular momentum transfer, SMBHs, gas outflow-inflow phenomena, etc.) make difficult the definition of an unambiguous evolutionary sequence. For spheroids, the astrophysical processes seem to be dominant. As has been emphasized by Renzini (1994), to reveal the complexity of galaxy evolution the deductive approach has to go necessarily together with the inductive one.

Great perspectives are open for further research in galaxy formation and evolution. A better understanding of all kinds of astrophysical processes involved in the evolution of galaxies is crucial. Star formation, hydrodynamics and feedback are among the most relevant, in particular, for spheroids. A better modelling of the luminous objects which form within the dark halos, will allow us to use the observational properties of galaxies to trace the physical conditions of the early universe and dark matter. From the astrophysical side, the connection of spheroid formation to ULIGs, submillimeter sources and QSO-AGN phenomenon is an appealing problem. The interplay of galaxy evolution with the IGM is also an important avenue of research.

As Ivan King said sometime ago, the main challenge is reserved for those who obtain results linking theory and observations; they are the astronomers.

This work was supported by CONACyT grant 33776-E to V.A.

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