J. Hartle, "Gravity: an introduction to Einstein's general relativity" -- easy reading, good at undergrad level.
B. Schutz, "A first course in general Relativity" -- easy reading, good at undergrad level.
Misner, Thorne, Wheeler, "Gravitation" -- very comprehensive, graduate level book with various useful things (incl. problems).
R. Wald, "General Relativity" -- more recent comprehensive graduate level book, also with problems.
Landau and Lifshitz, "Classical theory of fields", Course of Theoretical physics, vol.2 -- classic, as the others in the series.
M. Nakahara, "Geometry, Topology and Physics" -- useful for various mathematical aspects.
Rough outline: reviewing special relativity, setting notation for curved spacetimes, approximations to Newtonian gravity incorporated with special relativity, general coordinate invariance and the principle of equivalence, some differential geometry, operational descriptions of trajectories in curved spacetimes, the example of timelike/null orbits in the Schwarzschild spacetime, more geometry (tensors, covariant derivatives, geodesic deviation, curvature), Einstein's equations, the stress-energy tensor, solutions, curvature 2-form techniques, rudiments of gravitational waves, black holes (Schwarzschild black holes, causal structure, Kruskal and Penrose diagrams, singularities, charged black holes, thermodynamics), the cosmological constant and deSitter space, cosmology (basic data, homogeneity/isotropy, FRW solutions and their cosmology, the Big-Bang singularity, a brief history of the Universe (the standard model of cosmology), inflation).
Midsem exam, 35%,
Term-paper, 15% (no assessed homework -- incorporated into the classes and tutorial sessions)
Endsem exam, 50%,
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