For a long time after the discovery in 1964 by Christenson, Cronin, Fitch and Turlay that the long-lived neutral kaon decays both into three and into two pions, which has since been taken as proof of CP violation, successive new and more precise experiments confirmed the original evidence and provided results compatible with a phenomenolog- ical description confining the CP violation to the mixing between neutral kaons and antikaons. However, the Standard Model, with three generations of quarks, linking as it does CP violation to the presence of a single non-trivial phase in the Cabibbo-Kobayashi-Maskawa quark mixing matrix, implies that if CP violation exists at all, then it is a general property of weak interactions, appearing in transitions where amplitudes involving all three quark families interfere with each other, producing effects with a mag- nitude related to that of the CKM coefficients.This fact has stimulated an impressive amount of theoretical work, leading in many cases to precise predictions. In parallel with the progress in the theory, more refined and much more powerful experiments have been specifically designed and performed in laboratories around the world, culminating with the construction of ad hoc accelerator facilities and detectors at Frascati, KEK and SLAC.

The first evidence for CP violation beyond the realm of kaon mixing which was intensively searched for was “direct” CP violation in the decay of neutral kaons to two pions. It took a succession of increasingly more sophisticated experiments to finally uncover it and in fact, after a first evidence in 1987 by NA31, it was firmly established only in 1999 by KTeV and NA48. In this case the theoretical complications in evaluating the effect prevent, still now, a real quantitative comparison of the experimental result with the Standard Model.

In the B meson sector, theoretical calculations are in some cases more reliable and in the last few years an extraordinary wealth of experimental results has been obtained by the BELLE and BaBar collaborations, yielding an overall impressive confirmation of the Standard Model and, at least up to now, only some possible hints of physics beyond it.

In neutrino physics, the recent discovery of flavour oscillations, with the implication that neutrinos have masses different from zero and violate lepton number conservation in their time propagation, has opened new scenarios, including the possibility of CP violation in the leptonic sector. Finally, the cosmological origin of the present unbalance between matter and antimatter in the Universe must have its roots on the violation of symmetry under CP and the explanation in terms of properties of the fundamental constituents of matter and their interactions is till today an open challenge.

Recognizing that the present was an appropriate time to review the field, from both the theoretical and experimental point of view, while planning for the forthcoming ex- perimentation at LHC and considering possible new facilities for kaon, B meson and neutrino physics, the SIF Council decided to support the proposal of devoting to CP violation the CLXIII Course of the “Enrico Fermi” International School of Physics. The task has been taken up by lecturers and seminar speakers who are leading researchers in the field. Collectively, and with the active participation of the students attending the School, a comprehensive in-depth review was critically carried out and we hope that the written version of the talks, presented in these proceedings, will serve as useful reference also for other researchers engaged or planning to enter in this exciting field of physics.

Lectures were given by H. Aihara, I. Bigi, P. Bloch, E. Blucher, A. Dolgov, J.J. Gomez-Cadenas, L. Lanceri, L. Littenberg, A. Masiero, A.I. Sanda and M.S. Sozzi, and seminars by R. Battiston, J.N. Butler, F. Costantini, A. Di Domenico, M. Giorgi, D. Hitlin, N. Ramsey and F. Bucci. We thank them all for their efforts in preparing the material for their careful and inspiring presentations, for the explanations during the discussion session and more generally for contributing to the lively atmosphere of the School. A well deserved thank is due for the timely preparation of the written text; unfortunately the written version of one of the seminars could not be included in these proceedings.

The dedicated work before, during and after the School, of the scientific secretaries Flavio Costantini and Marco Sozzi, was essential for the outcome.

Finally we thank Barbara Alzani for her invaluable help in the logistic preparation of the course and in making sure that everything went smoothly, as well as the local staff: G. Bianchi-Bazzi, R. Brigatti and L. Corengia; the help and patience of Marcella Missiroli were crucial for the completion of this volume.

Financial support to the School from INFN, the University and the Scuola Normale Superiore of Pisa is gratefully acknowledged.

M. GIORGI, I. MANNELLI AND A. I. SANDA