The School of Cosmology and Gravitation consists of the study of the universe in its immense entirety. One statement of cosmology sees the universe of galaxies as a kind of diffuse fluid in which the galaxies themselves play the role of fundamental particles. Modern cosmology is based on Einstein’s famous work on general relativity. Early cosmological models were based on this new theory of gravitation. Einstein was guided in his work by Mach’s principle that the inertial properties of matter are determined by the behavior of matter on a cosmic scale. As it developed, cosmology, beginning with cosmological models based on the general theory of relativity, continued to grow into a broader and at the same time more specialized branch of physics. After Hubble and Humanson’s discovery of the red shift of spectral lines in distant galaxies and its subsequent interpretation in terms of the general expansion of the universe, models of the universe that imply a singular initial state have prevailed. These models assure that it is completely meaningless to investigate the behaviour of the universe before this point. An alternative hypothesis has also been proposed, involving a stationary universe in which the constant creation of matter is assumed to compensate for its dispersion during the expansion of the universe. It is obvious that in this case one cannot speak of an age of the universe. Instead, one can speak of an average age of a part of the universe. The hypothesis of the universe as a steady state seems to have been contradicted by recent discoveries and observations, particularly the cosmological interpretation of the red shift of quasars and the background radiation. The acceptance that the very large red shifts of quasars are cosmological leads to the conclusion that quasars are the most distant objects ever observed. This would in turn lead to the conclusion that the universe was in the past different from its present state. The discovery of the background radiation in 1965 (its existence was predicted by Gamow as early as 1948) seems to imply the existence of a very hot initial state, similar to that hypothesized in big-bang theories, of which the background radiation is a remnant. Here begins speculation about the early stage of the universe, particularly when, as Gamow pointed out in 1948, radiation predominated over matter. The study of blackbody radiation at high temperatures (between 400 and 1000 MeV), where strong interactions play a key role between pions, nucleons, and antinucleons, seems to be of primary importance. At these high temperatures, blackbody radiation consists of photons, electrons, positrons, neutrons, muons, pions, nucleons, antinucleons and perhaps kaons and hyperons. In discussing the thermal equilibrium at this stage of the universe, strong interactions must be taken into account. It is easy to see the value and importance of studying elementary particles in a course on cosmology and cosmological models. It is also quite easy to understand the importance of also studying those stages in the development of the universe in which the presence of a high neutrino density was important; it seems that, because of the viscosity of neutrinos, even a highly anisotropic universe soon becomes isotropic. Another very interesting topic concerns the origin of galaxies and the related problem of the intergalactic medium. However, this problem requires knowledge of plasma physics. This aspect of cosmology and the related problem of angular momentum deserve great attention. Attention should also be paid to the discovery of gravitational waves, which, because of cosmological implications, allow some interesting speculations about what happens in the cores of galaxies. Some galactic cores, besides being strong emitters of infrared radiation, show the occurrence of extremely violent events; all these phenomena suggest that superdense matter, collapsed matter or black holes must exist in galactic cores. The cosmological problems raised by the recent discoveries are numerous. Many important branches of the physical sciences are brought together in cosmology, such as elementary particle physics, thermonuclear reactions, superdense matter, and many fundamental concepts such as the geometry of space-time, Mach’s principle, the direction of time, and others.