The theory of Special Relativity, although a century old, it is still a theory which has yet a long way to go. Special Relativity is the ground on which Particle Physics and General Relativity are based and constitutes an everyday laboratory practice. It is therefore important that the new physicist will understand it properly and deeply, while at the same time will be able to use it effectively as a working tool. The first part of this book develops the necessary mathematics with emphasis on tensor analysis and differential geometry on the flat Minkowski space, and contains useful material that can serve as a quick reference tool as well. It introduces the student into tensor analysis and the mathematical formalism required to manipulate Minkowski space-time. The reader will appreciate the geometric intuition incorporated into the standard algebraic index formalism and later on, the fact that the mathematics introduced is an adequate background for a smooth entrance into General Relativity, Astrophysics and Theoretical Physics. The second part of this book begins with the conceptual foundations of the theory and in the later chapters applies the mathematics of the first part to the study of a variety of important physical problems including electromagnetism. The approach is fully covariant with many worked out examples. It presents the relativistic collisions in a new geometric way and prepares the student for the next steps into Quantum Mechanics and General Relativity. This book develops the conceptual foundations of Special Relativity and couples the mathematics with the physical considerations and applications. There is an interplay between mathematical ideas and physical principles and arguments, each subject preserving its own individuality whereas at the same time creating a consolidated unit. Emphasis is given to the reasoning which elucidates the structure of the theory. Studying the contents of this book willmake the reader appreciate Special Relativity both as a conceptual theory of Space-Time Physics and as a working tool in the laboratory. Both aspects are required in order to enter successfully the more advanced areas of Quantum Mechanics, Particle Physics and General Relativity required at the later stages of the studies.