Lecture 1 (21.09.22): Introduction, pointillisme, notions of set, topological space, topological manifold, smooth manifold, semi-Riemannian manifold.
Lecture 2 (28.09.22): History of the relation between geometry and physics, focusing on Aristotle.
Lecture 3 (05.10.22): Aristotelian spacetime, Aristotelian laws, Galilean principle of relativity, Galilean spacetime, Galilean group, Newton laws, affine space, Euclidean structure.
Lecture 4 (12.10.22): Aether, Maxwell's equations, the constancy of speed of light in vacuum, Minkowski spacetime, Lorentz and Poincare groups, special relativity of Einstein, semi-Riemannian structure.
Lecture 5 (19.10.22): Relativity of simultaneity, hyperplanes of simultaneity in Minkowski spacetime, time dilation, length contraction, twin paradox, topological manifold, smooth manifold, ring of smooth functions, fiber bundle, sections of a fiber bundle.
Lecture 6 (26.10.22): Vector, tangent and cotangent bundles, module structure of sections of a fiber bundle, tensor, vector field, Lie bracket, p-form, Lie derivative, exterior derivative, interior product, metric, affine connection, metric-affine geometry, torsion, curvature, non-metricity.
Lecture 7 (02.11.22): A closer look on Lecture 6 topics, connection, torsion, curvature and non-metricity forms, Cartan structure equations, Levi-Civita connection, fundamental theorem of Riemannian geometry, Koszul formula, Schouten decomposition, classification of metric-affine geometries.
Lecture 8 (16.11.22): Review for midterm.
Lecture 9 (23.11.22): Linear algebra review, local frames and coframes, tensor components, evaluation of torsion, curvature and non-metricity components, connection coefficients.
Lecture 10 (30.11.22): Hodge star isomorphism, exterior derivative, calculations on coordinate frames, reconstruction of 3D calculus operators (div, curl, grad, scalar product, vector product) in terms of exterior derivative, Hodge star and wedge product.
Lecture 11 (07.12.22): Induced metric on 2D sphere, calculation of Levi-Civita connection coefficients on 2D sphere in two different local frames.
Lecture 12 (14.12.22): Ricci tensor, Ricci scalar, Einstein tensor, Einstein field equations, Ricci-flatness, Schwarzschild black hole solution.
Lecture 13 (21.12.22): Autoparallel curve, geodesic, geodesic equation, reparametrization of autoparallels, projective structure, conformal structure, Newtonian limit.
Lecture 14 (14.01.23): Student presentations, closing remarks.