This book examines in detail the classical theory of relativistic many-body dynamics using a world time for self-consistency, completeness, and possible critical experiment. The theory, originally by Stueckelberg, and generalised to the many-body system by Horwitz and Piron, allows solutions for the special relativistic system with long-range interaction in a manifestly covariant Lagrangian and Hamiltonian fashion. The covariant Kepler problem is considered in particular. Audience: This volume will be of interest to researchers whose work involves relativity and gravitation, electromagnetic theory, theoretical astrophysics, classical mechanics or space dynamics. It is also recommended as a text for an advanced-level graduate physics course in classical mechanics.