The purpose of this book is to provide a pedestrians route to the physics of many-particle systems. The material is developed along simple and generic models which allow to illuminate the basic mechanisms beyond each approach and which apply to broad variety of systems in different areas of physics and chemistry. The book is sorted in steps of slowly increasing complexity of the models. Complementing numerical tools help to carry on where analytical methods reach their limits. They provide at the same time a useful training for the typical numerical methods in many-body physics.In order to confine the huge field, we shall focus the discussions on finite systems wherefrom we take the examples of applications. This covers nuclei, atoms, molecules and clusters. The idea of this book is to concentrate first on the generic, robust and simple, approaches and show how they apply to several domains across the specific disciplines. On the other hand, we aim to establish contact with actual research by carrying forth some examples up to realistic applications. This latter aspect emphasizes our intention to guide the reader in practizing the tools presented in the book, both at schematic and realistic levels.

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