Our vision of the cosmic world and in particular of the whole Universe has been changing dramatically in the last century. As we will see, galaxies were repeatedly the main protagonist in the scene of these changes. It is about 80 years since E. Hubble established the nature of galaxies as gigantic self-bound stellar systems and used their kinematics to show that the Universe as a whole is expanding uniformly at the present time. Galaxies, as the building blocks of the Universe, are also tracers of its large-scale structure and of its evolution in the last 13 Gyrs or more. By looking inside galaxies we find that they are the arena where stars form, evolve and collapse in constant interaction with the interstellar medium (ISM), a complex mix of gas and plasma, dust, radiation, cosmic rays, and magnetics fields. The center of a significant fraction of galaxies harbor supermassive black holes. When these "monsters" are fed with infalling material, the accretion disks around them release, mainly through powerful plasma jets, the largest amounts of energy known in astronomical objects. This phenomenon of Active Galactic Nuclei (AGN) was much more frequent in the past than in the present, being the high-redshift quasars (QSO's) the most powerful incarnation of the AGN phenomenon. But the most astonishing surprise of galaxies comes from the fact that luminous matter (stars, gas, AGN's, etc.) is only a tiny fraction (~ 1 - 5%) of all the mass measured in galaxies and the giant halos around them. What this dark component of galaxies is made of? This is one of the most acute enigmas of modern science.
Thus, exploring and understanding galaxies is of paramount interest to cosmology, high-energy and particle physics, gravitation theories, and, of course, astronomy and astrophysics. As astronomical objects, among other questions, we would like to know how do they take shape and evolve, what is the origin of their diversity and scaling laws, why they cluster in space as observed, following a sponge-like structure, what is the dark component that predominates in their masses. By answering to these questions we would able also to use galaxies as a true link between the observed universe and the properties of the early universe, and as physical laboratories for testing fundamental theories.
The content of these notes is as follows. In Section 2 a review on main galaxy properties and correlations is given. By following an analogy with biology, the taxonomical, anatomical, ecological and genetical study of galaxies is presented. The observational inference of dark matter existence, and the baryon budget in galaxies and in the Universe is highlighted. Section 3 is dedicated to a pedagogical presentation of the basis of cosmic structure formation theory in the context of the Cold Dark Matter (CDM) paradigm. The main questions to be answered are: why CDM is invoked to explain the formation of galaxies? How is explained the origin of the seeds of present-day cosmic structures? How these seeds evolve?. In Section 4 an updated review of the main results on properties and evolution of CDM halos is given, with emphasis on the aspects that influence the propertied of the galaxies expected to be formed inside the halos. A short discussion on dark matter candidates is also presented (Section 4.2). The main ingredients of disk and spheroid galaxy formation are reviewed and discussed in Section 5. An attempt to highlight the main drivers of the Hubble and color sequences of galaxies is given in Section 5.3. Finally, some selected issues and open problems in the field are resumed and discussed in Section 6.