Introduction to the Proceedings of the 9

\nThis introduction to these proceedings is mainly devoted to comment a few intermediate models. The interest of intermediate models lies in their ability to define large classes of entities, and such general principles can go through distinct disciplines, the main goal of these days. The first examples of intermediate models with short range interactions are shown to occur in magnetism. This practical knowledge is then transferred to the case of structures where geometry and energy compete in defining crystals, quasicrystals and more disordered structures. Such studies based upon a simple variational treatment followed by a careful relaxation using classical numerical treatments enable us also to deal with defects, static and dynamic surface problems. This classification of structures leads also to classify metallic atoms. The rich field of lacunary systems and alloys is also evocated with its potential links with sociology for instance. Finally, long-ranged interactions such as dipolar ones are introduced as intermediate models. These dipolar interactions are sensitive to the size and shape of the sample and act even through vacuum between disconnected parts. This introduces a full complexity with rich static and dynamic properties. Finally, all contributions are briefly introduced.\n