In the standard cold dark matter model, galaxy formation occurs hierarchically. At least this is what happens to the dark matter component, that collects into ever-larger structures (the halos mentioned above) via a process of gravitational interaction and successive merger. Although driven gravitationally by dark matter, what happens to the baryonic component could be very different. In general it is thought that the latter collapses in the potential wells created by dark matter, in what is called dissipative collapse, converting primordial gas into stars. This could be the origin of the most massive galaxies, the ellipticals, and in general of the spheroidal component observed in spiral galaxies. In this latter case, the disks form around the spheroid as the result of a slow and continuous acquisition of gas from the regions around the galaxy. This gas acquires angular momentum and contributes to the formation of the younger stellar population, as well as providing the fuel for successive generations. In this process, both the initial mass of the dark matter halo in which the galaxy forms and the environment in which it finds itself play an important role. It is well established, for example, that in galaxy clusters, or in regions of high density, the fraction of spiral galaxies is very low. The last 15 years have seen great progress in this field, with an important contribution from the Italian astronomical community both through the above mentioned surveys, VVDS and COSMOS-ZCOSMOS, and other projects (for example GMASS and GOODS), equally important for the understanding of the evolutionary phenomena that guide the history of the galaxies. On this qualitative picture there is general agreement, even if details such as the epoch of formation of disks or the relative role of mass and environment in defining the properties of forming galaxies are still poorly defined, also due to the dearth of available samples at redshift z>1.5-2.

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