Conventional observations in cosmology, together with the recent discovery of collapsed objects in our galaxy, have provided clear evidence for the existence of processes in which both special and general relativistic effects are of fundamental importance. Far from contributing only minor corrections and negligible effects, general relativity provides the basic theoretical framework for the complete description of these physical processes. Relativistic astrophysics has therefore become the ideal field of research to study and probe the deeper implications of the space-time description of general relativity. The aim of this School is to analyse, both from a theoretical and experimental point of view, the multiple aspects of the extreme conditions of matter encountered in these ultra-relativistic regimes. The subject ranges from the analysis of nuclear and elementary particle physics (necessary for the description of the equilibrium configuration of a neutron star or the core of a normal star in its last stages of evolution), to the analysis of the processes of relativistic magnetohydrodynamics or the physics of the plasma that occurs in the magnetosphere of collapsed objects. An important effort is directed towards relativistic invariant formulations of problems and general schemes that, far from providing only phenomenological answers, can open new main directions of research. Similarly, in the experimental field, topics range from the analysis of terrestrial observations (made with radio- interferometers and optical telescopes) to observations made in the X-ray, gamma-ray, or infrared band by satellites. Special emphasis is also placed on theoretical programmes of great conceptual interest, even if they lack direct experimental verification. This promotes the in-depth analysis of possible alternatives to Einstein’s theory of gravitation; this is done together with new formulations of the traditional theory with the help of particularly attractive mathematical techniques (e.g. spinor formalism, twistors, Regge calculus, etc.), or problems of great intellectual fascination (such as field theories in curved backgrounds), or the quantisation of the gravitational field (e.g., Dirac’s work, Christodoulou’s approach, or new theoretical developments of Riemann’s classical ideas). Similarly, in the experimental field, progress is represented by techniques that have not yet achieved definitive success. Examples are the detection of gravitational radiation or the detection of other transient phenomena in electromagnetic radiation or neutrino interactions that could be related to the gravitational collapse process. The course will be presented in a systematic manner, geared towards following Bianchi’s classical work and the great progress made later in this field in solving cosmological problems. Models of universes with anisotropy and rotation will be presented, following the powerful and general attack proposed by Gödel, Schucking, Ozsvath and Jantzen. Consequently, in the experimental field the focus will be on objects with red-shift z > 2.