## ABSTRACT

E=mc² is known as the most famous but least understood equation in physics. This two-volume textbook illuminates this equation and much more through clear and detailed explanations, new demonstrations, a more physical approach, and a deep analysis of the concepts and postulates of Relativity. The first part of Volume I contains the whole Special Relativity theory with rigorous and complete demonstrations. The second part presents the main principles of General Relativity, including detailed explanations of the bending of light in the neighborhood of great masses, the gravitational time dilatation, and the principles leading to the famous equation of General Relativity: D(g) = k .T. The most important cosmological predictions are then described: the Big Bang theory, black holes, and gravitational waves. Plentiful historical information is contained throughout the book, particularly in an ending chapter depicting the scientific and epistemological revolution brought about by the theory of Relativity. Volume II progresses into further depth than Volume I, and its scope is more extended than most introductory books on Relativity. It includes the affine connection, the geodesic equation, and an introduction to cosmological models. The mathematical tools dedicated to Relativity are carefully explained for those without an advanced mathematical background (tensors, Lagrangians, covariant derivative). Both volumes place an emphasis on the physical aspects of Relativity to aid the reader’s understanding and contain numerous questions and problems (147 in total). Solutions are given in a highly detailed manner to provide the maximum benefit to students. This textbook fills a gap in the literature by drawing out the physical aspects and consequences of Relativity, which are otherwise often second place to the mathematical aspects. Its concrete focus on physics allows students to gain a full understanding of the underlying concepts and cornerstones of Relativity.

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**Volume 1:** 1. Relativity of Time and Distance 2. The Lorentz Transformation 3. Other New Kinematics Laws, Causality and Accelerated Trajectories 4. The Next Revolution: Dynamics 5. The Energy Revolution: E = MC²γ and Its Consequences 6. Introduction to General Relativity 7. Cosmological Consequences 8. Epilogue: A Scientific and Epistemological Revolution 9. Solutions to Questions and Problems

**Volume 2: **1. Steps Before the Lorentz Transformation 2. The Lorentz Transformation. the New Metric and Accelerated Objects 3. The Relativistic Laws of Dynamics 4. Introduction to General Relativity 5. Important Consequences 6. Introduction to Cosmological Models 7. Further Axiomatic Considerations 8. Answers to the Questions and Exercises