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, i.e. classical or quantum systems of charged particles interacting exclusively with the Coulomb force, drawing on results that are mathematically rigorous or derived from formal perturbation series, without ad hoc modeling or intermediate approximations. Two main themes form the essential purpose of Statistical Mechanics of Coulomb Systems: the simplified description of the proofs of four fundamental theorems on the existence of Coulomb matter on the one hand and the development of a formalism based on diagrammatic expansions adapted to the treatment of classical and quantum screening phenomena on the other hand. The result is an authoritative analysis of Coulomb systems that will be essential for any physicist working in this area.