The purpose of the CXXXVIII Course of the Varenna School has been to unfold the matter of nuclei. It so happened that its occurrence coincided with the centennial of both the Italian Physical Society (SIF) to which one of us (RAR) has dedicated a special issue and the discovery of Becquerel, which marked the beginning of nuclear physics. It is appropriate to remind, in this connection, that of the one hundred and thirty-eight Courses held in Varenna a good twenty focussed on nuclear physics and related domains. Indeed the SIF has not escaped the confrontation with the challenging problem of the nucleus and of its constituents.

Beyond the celebrative purpose a question, however, arose: was it necessary one more Course on the subject? The organizers believed it was, chiefly on two counts:

a) the growing extension undergone by nuclear physics,

b) the deepening in the understanding of the physics of the nucleus and of its constituents lately achieved.

Concerning the broadening of the themes addressed by nuclear physics it goes without saying that it could hardly have been foreseen, not only at the Becquerel time, but even three or four decades ago. The search for signatures of the quarks in nuclei with electromagnetic probes and, at much higher energies, for signatures of the quark-gluon plasma in ultrarelativistic nuclear collisions are here the best examples. They were authoritatively discussed in the lectures of Helmut Satz, who provided a comprehensive account of the second subject, and of Bernard Frois, who dealt with the former one in the broader context of the electromagnetic interaction with the nucleus and the nucleon.

In this respect, however, a remark might be appropriate: at the School, quarks were not viewed as the basic constituents required for improving the understanding of nuclei as commonly encountered in nature. Indeed, as we, by and large, need not nuclear physics to control the atomic structure, likewise we can satisfactorily cope with nuclei up to some energy (say 1–2 GeV) in terms of nucleons and mesons, or even, in the few MeV domain, in terms of bosons without recurring at all to the QCD degrees of freedom: a point convincingly stressed by Nathan Isgur, whose absence was much regretted in Varenna.

But the question related to where the transition from one set of degrees of freedom to the other occurs is too fundamental to be ignored by modern physics and nuclei represent a marvellous laboratory to explore it: how the transition takes place? where? Certainly well before QCD lends itself to be perturbatively treated. What are then the best approaches to the non-perturbative QCD? This crucial issue was masterly treated by Frank Close, who gave fascinating examples of the quark and gluon structure of the matter.

Another point to realize is that, in its broadening, nuclear physics is stretching itself not only on the high-energy frontier, but also in the direction of attempting to obtain new nuclei in the laboratory. The spell of the quest for the island of superheavy elements was extensively conveyed to both the young and senior attendants of the School by Peter Armbruster and Yuri Oganessian.

In parallel to widening the set of addressed issues, nuclear physics is also expanding its impact on other domains of physics: an impressive example of this was presented in the lectures of Jean Vervier on nuclear astrophysics.

Likewise the beautiful, hystorically framed, lecture of Samoil Bilenky brought to evidence the central role played by nuclear physics in the development of weak interactions: indeed the importance of the β-decay of He³ , of the nuclear ββ-decay, of the elastic neutrino nuclear scattering in connection with fundamental issues of neutrino's physics can hardly be overstated.

Progress in all the items above referred to ultimately rests on a deeper theoretical handling of the nuclear and nucleon's structure. The latter, in addition to the specific models presented in Close's lectures, can also be addressed by relying on numerical (exact as far as possible) solutions of QCD on a discrete space-time lattice. The prodigious advancement of the computational capabilities has spurred a growing interest in this approach although nuclei remain, likely for a long time and as far as an exact solution is concerned, out of reach of computers. The topic was skillfully addressed by John Negele with lectures both of great scientific interest and pedagogical value. He also explored alternative routes for solving non-perturbative QCD: in particular the promising instanton's one.

Yet different paths toward solving non-perturbative QCD were followed by Fabrizio Palumbo. He rigorously investigated the difficult and longstanding problem of how to merge fermion fields into bosonic and fermionic composites, confronting both the case of two (three) quarks combining into mesons (nucleons) and of nucleons joining into the Iachello bosons.

In ascending the ladder of complexity from the nucleon to the nuclear many-body problem, we encounter the very interesting and highly instructive lectures of Arthur Kerman and Hans Weidenmüller. They shared a common trait: the one of framing the nuclear problem in the broader context of general many-body physics. The long borderline between nuclear and condensed matter physics of course has long been recognized. In Varenna it was enlightened by a novel light: first by showing how the physics of mesons, nuclei and condensed atomic bosons, like the ones recently captured in a magnetic field, can be unifyied by the powerful methods of quantum field theory (Kerman) and then by disclosing the variety of apparently disconnected fields of physics which are actually encompassed by the random matrix theory (Weidenmüller). In connection with the last item one cannot avoid regretting the greatly missed presence of Herman Feshbach. He was expected to deal with the theory of nuclear reactions, the field he has founded. When time delays in nuclear reactions are long, then the randomness sets in. We can only imagine how enriching for all of us would have been to witness a confrontation of the lines of thought of Feshbach and Weidenmüller.

In ending this overview of the School we encounter the lectures of Franco Iachello and Igal Talmi. To comply with the hystorical perspective they should have been placed at the beginning, as was done in Varenna; in the above mentioned scale set by complexity, they should stay at the end. Iachello's theory, founded on beautiful symmetries, which are realized through powerful algebraic relations, stands today as the cornerstone of the field. It catches the regularities that, in spite of their complexity, nuclei exhibit in their spectra with astonishing success. This, in turn, renders more acute the desire for a deeper understanding of its microscopic foundation.

Here lies the link with Talmi lectures. The shell model, almost 50 years old, is still conceptually surprising. Even more, it holds surprises for the future: such in fact is the complexity of nuclear spectra. The basis of the interacting boson model are searched in the frame of the shell model.

We cannot conclude this foreword without warm thanks to the seminar speakers: W. M. Alberico, who nicely complemented the Satz lectures, T. Bressani, A. Covello, M. Pignanelli and N. Cindro. They also importantly contributed to the success of the School.

Finally the generosity and wisdom of INFN, in particular of its President L. Maiani, who allowed the School to benefit from the exchange agreement INFN-MIT, are deeply acknowledged.

A. Molinari and R. A. Ricci