Superconductivity is undoubtely one of the most exciting fields in the physics of the present century both from the experimental as well as from the theoretical viewpoint. The discovery of new superconducting materials has pushed forward the development of experimental low-temperature physics. The search for microscopic models to explain the many superconducting substances has introduced seminal concepts and techniques in many-body physics and in statistical mechanics.

The properties of the new compounds in their normal state are just as puzzling as the superconducting phase properties were in the low-temperature conventional materials. The complexity of the high-temperature superconductors has required a remarkable refinement of experimental techniques in order to allow a reliable characterization of the samples, and this is partly the reason why so many different microscopic models have so far been proposed.

Although we were a priori convinced that it would not be possible to give a complete overview of all the topics related to superconductivity; nevertheless we hope that the present selection may be useful to young researchers who are entering this rapidly evolving field as well as to more experienced scientists.

The large volume of experimental and theoretical work and the lack of a generally accepted theoretical framework needed to understand high-T_c superconductivity has made the choice of the topics to be included in the Course difficult. Inasmuch as the School is named after Enrico Fermi, our first choice has been to give equal weight to experimental and theoretical topics. We focused our attention on those reliable measurements which are expected to provide the theory with key constraints, viz: Raman and Infrared Spectroscopy, Nuclear Spin Resonance, Angular Resolved Photoemission Spectroscopy, transport measurements, Josephson effect. From a pedagogical point of view, the purpose of the lectures is to provide the students with a general background on these techniques and then to focus on specific results relevant to the physics of super conducting materials.

The choice of the theoretical topics has been even more difficult. We believe that the lectures devoted to the overview of the BCS theory and to the discussion of minimal models and of the crossover from BCS to Bose-Einstein condensation may be particularly useful to students. The remaining part of the program is shared between phonon- and non-phonon-based mechanisms. On the one hand, special emphasis has been devoted to the breakdown of the Migdal theorem and to polaronic theories. On the other hand, the book contains an overview of strongly correlated electron theories, including magnetic interactions. A survey of the physics of vortices completes the theoretical part of the lectures.

The organization of the CXXXVI Course of the “Enrico Fermi” School, the choice of the topics and of the speakers bears the fruits of the enthusiastic participation of Sir Nevill Mott, who started with us along this way on June 1996. We believe to interpret the wish of everybody in dedicating this volume to his memory. It certainly contains a large part of his ideas and of his recent work on high-temperature superconductivity. For this reason the book opens with the lecture which Sasha Alexandrov has dedicated to his memory.

We wish to thank the Italian Physical Society (SIF) for financial and logistical support. We wish to thank the SIF Secretariat (in particular, Mrs. Enrica Mazzi) as well as the Editorial Staff for the much needed help with the local organization and with the publication of these Proceedings. We wish to thank all the lecturers for the enthusiasm with which they took part in the Course, fruitfully interacting with the participants. We thank them all who enthusiastically contributed to the success of the School and were not hampered by the inclement weather. We finally thank the Consiglio Nazionale delle Ricerche, the Gruppo Nazionale di Struttura della Materia of the CNR and the Istituto Nazionale di Fisica Nucleare for their sponsorship.

G. Iadonisi, J.R. Schrieffer and M.L. Chiofalo