A study of the equilibrium properties of Coulomb systems in physics that is the first of its kind. This book studies the equilibrium properties of Coulomb systems, namely classical or quantum systems of charged particles interacting purely with the Coulomb force, drawing on results that are mathematically rigorous or derived from formal perturbation series, without resorting to ad hoc modeling or phenomenological descriptions. It also includes the findings of ab initio numerical simulations, as well as a presentation of simple and accurate approximations. Exercises with corrections are proposed There are two main themes. The first aims to gather and summarize the demonstrations of fundamental theorems on the stability and extensivity of matter, the screening phenomena, and the existence of atomic and molecular phases. The second theme revolves around an in-depth analysis of the Coulombic correlations by means of diagrammatic series of Mayer type, that incorporate screening in a non perturbative way. This tool is well suited to low-density calculations of van der Waals forces and viral expansions in fully or partially ionized regimes. Considerations about the Kosterlitz-Thouless transition and phase transitions in simple models are also presented.

The book is the first of its kind, providing an authoritative text for any physicist working in this area.