The interacting boson model has emerged in the last fifteen years as a unified framework for the description of the collective properties of nuclei. The key ingredients of this model are its algebraic structure based on the powerful methods of group theory, the possibility it gives to perform calculations in all nuclei and its direct connection with the shell model that allows one to derive its properties from microscopic interactions.

The interacting boson model deals with nuclei with an even number of protons and neutrons. However, more than half of the nuclear species have an odd number of protons and/or neutrons. In these nuclei there is an interplay between collective (bosonic) and single-particle (fermionic) degrees of freedom. The interacting boson model was extended to cover these situations by introducing the interacting boson-fermion model. This book, which is the second in a series of three, describes the interacting boson-fermion model and its applications. It has two aspects, an algebraic (group-theoretic) aspect and a numerical one. The algebraic aspect describes the coupling of bosons and fermions. The situation here is by far more complex than in the case of eveneven nuclei and, for this reason, it is described in greater detail. The study of coupled Bose-Fermi systems is a novel application of algebraic methods and as such has a wider scope than that presented here. It has been used recently in other fields of physics, as for example in the coupling of electronic and rotation-vibration degrees of freedom in molecules.