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INTRODUCTION CHAPTER I EUCLIDEAN SPACE. ITS MATHEMATICAL FORM AND ITS ROLE IN PHYSICS. 1. Derivation of the Elementary Conceptions of Space from that of Equality 2. Foundations of Affine Geometry 3. "Conception of n-dimensional Geometry, Linear Algebra, Quadratic Forms" 4. Foundations of Metrical Geometry 5. Tensors 6. Tensor Algebra. Examples 7. Symmetrical Properties of Tensors 8. Tensor Analysis. Stresses 9. The Stationary Electromagnetic Field CHAPTER II THE METRICAL CONTINUUM 10. Note on Non-Euclidean Geometry 11. Riemann's Geometry 12. Riemann's Geometry (continued). Dynamical View of Metrics 13. Tensors and Tensor-densities in an Arbitrary Manifolds 14. Affinely Connected Manifolds 15. Curvature 16. Metrical Space 17. Remarks on the Special Case of Riemann's Space 18. Space Metrics from the Point of View of the Theory of Groups CHAPTER III RELATIVITY OF SPACE AND TIME 19. Galilei's and Newton's Principle of Relativity 20. Electrodynamics of Varying Fields. Lorentz's Theorem of Relativity 21. Einstein's Principle of Relativity 22. "Relativistic Geometry, Kinematics, and Optics" 23. Electrodynamics of Moving Bodies 24. Mechanics of the Principle of Relativity 25. Mass and Energy 26. Mie's Theory Concluding Remarks 27. "Relativity of Motion, Metrical Field, and Gravitation" 28. Einstein's Fundamental Law of Gravitation 29. Stationary Gravitational Field. Relationship with Experience 30. Gravitational Waves 31. Rigorous Solution of the Problem of One Body 32. Further Rigorous Solutions of the Statical Problem of Gravitation 33. Energy of Gravitation. Laws of Conservation 34. Concerning the Inter-connection of the World as a Whole 35. Word Metrics as the Origin of Electromagnetic Phenomena 36. Application of the Simplest Principle of Action Fundamental Equations of Mechanics APPENDIX I APPENDIX II BIBLIOGRAPHICAL REFERENCES INDEX

About the Author

Along with his fundamental contributions to most branches of mathematics, Hermann Weyl (1885-1955) took a serious interest in theoretical physics. In addition to teaching in Zurich, Gottingen, and Princeton, Weyl worked with Einstein on relativity theory at the Institute for Advanced Studies. Hermann Weyl: The Search for Beautiful Truths One of the most influential mathematicians of the twentieth century, Hermann Weyl (1885-1955) was associated with three major institutions during his working years: the ETH Zurich (Swiss Federal Institute of Technology), the University of Gottingen, and the Institute for Advanced Study in Princeton. In the last decade of Weyl's life (he died in Princeton in 1955), Dover reprinted two of his major works, The Theory of Groups and Quantum Mechanics and Space, Time, Matter. Two others, The Continuum and The Concept of a Riemann Surface were added to the Dover list in recent years. In the Author's Own Words: "My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful." "We are not very pleased when we are forced to accept mathematical truth by virtue of a complicated chain of formal conclusions and computations, which we traverse blindly, link by link, feeling our way by touch. We want first an overview of the aim and of the road; we want to understand the idea of the proof, the deeper context." "A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details." - Hermann Weyl Critical Acclaim for Space, Time, Matter: "A classic of physics ... the first systematic presentation of Einstein's theory of relativity." - British Journal for Philosophy and Science

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