"Version: 20180501"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.1. Introduction -- 2. Many-body relativistic mechanics and gauge theory -- 2.1. The classical two-body problem -- 2.2. The classical N-body problem -- 2.3. Electromagnetism3. Quantum mechanical two-body problem and consequences for many-bod…