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Explore the fundamental principles of general relativity in this comprehensive lecture delivered by Olivier Sarbach from Universidad Michoacana de San Nicolás de Hidalgo as part of the Fields Institute's General Relativity Winter School. Delve into Einstein's revolutionary theory of spacetime and gravitation through expert instruction designed for advanced students and researchers. Learn essential mathematical frameworks and physical concepts that form the foundation of modern gravitational physics. Gain insights into how mass and energy curve spacetime, leading to the phenomena we observe as gravity. Discover the geometric interpretation of gravitational fields and understand the mathematical tools necessary for analyzing relativistic systems. This opening lecture sets the stage for deeper exploration of topics including black holes, cosmology, and gravitational waves within the broader context of the thematic program on shocks and singularities in nonlinear evolution equations.
