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The 1972 Banff lectures attempted a systematic exposition of the ideas underlying recent developments in general relativity and its astronomical applications at a level accessible and useful to graduate students having some previous acquaintance with the subject. To our regret, it was not possible to include any printed record of Peebles' beautiful lectures on observational cosmology or of the many stimulating seminars on special topics contributed by the participants. What remains is nevertheless a reason ably self-contained and compact introduction to Einstein's theory in its modern in carnation, and we hope it will be found useful by the many physicists, astronomers, and mathematicians who wish to update and deepen their understanding of the theory. On behalf of the organizing committee, I should like to express appreciation to a number of people whose help was crucial to the success of the enterprise: to Jan van Kranendonk, who initiated the idea of a Banff summer school on general relativity; to him and to David Rowe and Don Betts for inspiration and moral support; to our indefatigable secretaries Olwyn Buckland and Leslie Hughes; and to Garry Nash, Richard Sigal, Tim Spanos, and Gordon Wilson who helped in a variety of ways to keep the wheels running. How much we owe to the splendid cooperative effort of the lecturers will be clear to any reader of the following pages.
Survey of General Relativity Theory.- 0. Introduction.- 1. Quasi-Historical, Empirical Motivation of the General Theory of Relativity.- 2. A Constructive-Axiomatic Approach to General Relativity Theory.- 3. Kinetic Theory.- 4. Continuum Mechanics and Thermodynamics.- 5. The Transition from Maxwell's Equations to Geometrical Optics.- 6. Note on the Dynamics of Extended Bodies.- 7. Approximation Methods.- 8. Spherically Symmetric Spacetimes.- References.- Observational Contacts of General Relativity.- 1. Introduction.- 2. Fundamental Properties of Gravity.- 3. Alternative Theories and Solar System Experiments.- 4. Experiments on Gravitational Radiation.- References.- Relativistic Stars, Gravitational Collapse, and Black Holes.- 1. Introduction.- 2. The Relativistic Stellar Structure of Spherical Stars.- 3. Spherically Symmetric Gravitational Collapse.- 4. Non-Spherical Gravitational Collapse and Black Holes.- 5. Black Hole Dynamics.- Acknowledgements.- References.- Cosmology.- 1. Introduction.- 2. General Methods.- 3. The Geometry of the Hot Einstein De Sitter Model.- 4. Evolution of the Hot Einstein De Sitter Model.- 5. Inhomogeneous Models.- 6. Homogeneous Anisotropic Spacetimes.- 7. Conclusion.- Acknowledgements.- References.- Canonical Quantization of Gravity.- 1. Parametrized Theories.- 2. Geometrodynamics.- 3. Quantization.- 4. Midi-superspace.- Acknowledgements.- Differential Geometry from a Modern Standpoint.- 1. Manifolds.- 2. The Tangent Space.- 3. Dual Space of the Tangent Space Tensors.- 4. Commutators and Exterior Derivative of Forms.- 5. Maps between Manifolds.- 6. Lie Groups and Lie Transformation Groups.- 7. The Frame Bundle of a Manifold.- 8. The Lie Derivative.- 9. Covariant Derivative - Linear Connection.- 10. Descriptions of a Linear Connection.- 11. Curvature Tensor and Structure Equations.- 12. The Connection Induced by a Metric.- 13. Geodesies.- References.- Index of Subjects.