The concept of symmetry in the Interacting Boson Model (IBM) description of even-even nuclei has proved to be one of the model's most important elements, because they provide benchmarks in the formulation of a unified description of a broad range of nuclei. The importance of the recently proposed symmetries in odd-even systems can thus be viewed in the same light, and their role in pointing to a simple prescription for the changing collective structure in odd A nuclei throughout a major shell is likely to prove even more essential, given the much greater complexity of the boson-fermion (IBFM) Hamiltonian. The group structure of a boson-fermion system is described by U/sup B/(6) x U/sup F/(m) where m specifies the number of states available to the odd fermion, and thus depends on the single particle space assumed. The ability to construct group chains corresponding to the symmetries SU(5), SU(3) or 0(6) depends on the value of m. Of the structures studied in detail to date, the case of m = 12 is the one with the broadest potential. The fermion is allowed to occupy orbits with j = 1/2, 3/2 and 5/2, so that the assumed single particle space corresponds to the negative parity states available to an odd neutron at the end of the N = 82-126 shell, namely, P12, p32 and f52. The region of interest thus spans the W-Pt nuclei, and since one prerequisite for an odd-A symmetry is the existence of that same symmetry in the neighboring even-even core nucleus, the odd Pt nuclei around A = 196 offer the obvious testing ground for the 0(6) limit of U(6/12). The heavier even-even W nuclei, on the other hand, have the characteristics of an axial rotor, and hence the negative parity structure of the neighboring odd W isotopes offers the possibility to study the validity of the SU(3) limit. Given a definition and understanding of these two limits, the construction of a simple description of the transitional Os nuclei can be considered.

The interacting boson-fermion model has become in recent years the standard model for the description of atomic nuclei with an odd number of protons and/or neutrons. This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. The book addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed. The book is the first comprehensive treatment of the subject and will appeal to both theoretical and experimental physicists. The large number of explicit formulas for level energies, electromagnetic transition rates and intensities of transfer reactions presented in the book provide a simple but detailed way to analyse experimental data. This book can also be used as a textbook for advanced graduate students.

Work on the unification of the fundamental particle interac tions has continued vigorously since the first Europhysics study Conference on this subject. At that time we emphasized the exis tence of two main approaches, one based on supersymmetry and pos sibly its local version, supergravity, and the other approach based on grand unified gauge theories. Discussion of the possible tests of these theoretical speculations included experiments on baryon decay and neutrino oscillations. In view of the uncertainties surrounding the observability of such phenomena, the early Universe was welcomed as a possible Laboratory for testing new theoretical ideas. At that time, we expressed the hope that the different gauge and super symmetry approaches would cross-fertilize each other" and it is appropriate to ask now how much of that hope has been realized. We believe there has recently been considerable theoretical rapprochement, which is amply reflected in these Proceedings. On the one hand it has been realized that many of the technical pro blems in grand unified gauge theories, such as arranging the hierarchy of different mass scales, may be alleviated using simple global supersymmetry. On the other hand there has been growing interest in the possibility that extended supergravity theories may furnish a suitable framework for the unification of all the fundamental particle interactions. Many physicists in fact now question actively whether the known "fundamental" particles are in deed elementary, or whether they are composite.