All elementary constituents of everyday matter (electrons, protons and neutrons) are fermions, named after Enrico Fermi who introduced, in 1925 in Florence, the quantum statistics of half-integer spin particles. The Varenna school, which carries the name of Enrico Fermi, has witnessed all major advances in physics since 1953. It has been a special honour for us to organize an Enrico Fermi school on Ultracold Fermi Gases, yet another striking development that even the great scientist could not anticipate.

The list of Varenna schools includes cornerstone courses in atomic physics. After the milestones of laser spectroscopy, the fast advances in the field of cold atoms were timely covered by the 1991 School on Laser Manipulation of Atoms and the 1998 School on Bose-Einstein Condensation in Atomic Gases. Following this tradition, the School on Ultracold Fermi Gases highlighted new developments and discussed exciting new directions. These three summer schools on cold atomic gases mark three distinct periods in the exploration of the ultralow temperature regime.

The field of cold atomic gases faced a revolution in 1995 when Bose-Einstein condensation was achieved. Since then, there has been an impressive progress, both experimental and theoretical. The quest for ultra-cold Fermi gases started shortly after the 1995 discovery, and quantum degeneracy in a gas of fermionic atoms was obtained in 1999. The Pauli exclusion principle plays a crucial role in many aspects of ultracold Fermi gases, including inhibited interactions with applications to precision measurements, and strong correlations. The path towards strong interactions and pairing of fermions opened up with the discovery in 2003 that molecules formed by fermions near a Feshbach resonance were surprisingly stable against inelastic decay, but featured strong elastic interactions. This remarkable combination was explained by the Pauli exclusion principle and the fact that only inelastic collisions require three fermions to come close to each other. The unexpected stability of strongly interacting fermions and fermion pairs triggered most of the research which was presented at this summer school. It is remarkable foresight (or good luck) that the first steps to organize the summer school were already taken before this discovery. It speaks for the dynamics of the field, how dramatically it can change course when new insight is obtained.

This summer school took place after the quest for fermionic superfluidity with ultracold atoms has reached its goal, and high-temperature superfluidity was established in ultracold and ultradilute gases. These new superfluid atomic systems provide an ideal laboratory for investigating quantum many-body phenomena. Atomic physics brings to many-body physics the remarkable control and tunability of interactions, as well as of the spatial order provided by atom traps and optical lattices. This approach has stimulated an explosion of theoretical and experimental advances in the quantum physics of many-body systems. We are witnessing an important convergence of research efforts dealing with open problems in many-body physics, covering fields as diverse as high-energy physics, condensed matter, astrophysics, quantum information, and of course quantum gases.

This school brought together many leaders in both the theory and experiments on ultracold Fermi gases as well as a very large number of enthusiastic students from all over the world and from different fields of research. The lectures, which are written up in this volume, provided a detailed coverage of the experimental techniques for the creation and study of Fermi quantum gases, as well as the theoretical foundation for understanding the properties of these novel systems. Many exciting aspects were presented, including basic static and dynamical properties, molecule formation, superfluid behaviour and BEC-BCS crossover, fermions in optical lattices, and Fermi-Bose mixtures. The timing of the school was excellent since the field is still small enough to be fully covered, but it is also undergoing a major expansion.

This volume provides the first systematic review of the many developments that have taken place since the early beginnings of the field less than a decade ago.

The exciting scientific program of the School was enhanced by the special atmosphere of Lake Como combining in a unique blend water and mountains with historical tradition and culture. We warmly thank our scientific secretary, Francesca Ferlaino for her enthusiastic support, and Barbara Alzani for the professional organisation and her dedication which were crucial to the success of the school.

M. Inguscio, W. Ketterle and C. Salomon