The structure of matter is intimately related to the fundamental role played by many-fermion systems. The development in the last few decades of the microscopic many-body theory of correlated fermion systems has been a fertile ground not only for spectacular achievements in basic science in various areas of research, but also for technological applications. Among the numerous phenomena discovered and studied in systems of many fermions, one can cite the superconductivity in metals, the superfluidity in 3He, nuclear matter and nuclei, the quantum Hall effect, the giant resonances in nuclei, the Anderson location and the metal-insulator transition, hole and electron diffusion in doped semiconductors, etc. All these phenomena can be understood only in terms of correlations occurring in many-fermion systems, and the formulation of the correct microscopic theory of each phenomenon has marked a milestone in pure science as well as the starting point for the exploitation of its potential technological applications. It is likely that in the future further developments will take place in this field of basic science.The Hispalensis International School is a summer school aimed mainly at young physicists, both theoreticians and experimentalists, engaged in research work at the predoctoral or recent postdoctoral level. The objective of the School provide an opportunity for participants to come into contact with experienced researchers and hear their clear account of the state of the art of many-body theories in nuclear physics, as well as in related fields, and the main future lines of development.