Lecture 1 (16.02.2026): Introduction, syllabus
Lecture 2 (23.02.2026): Pointillisme, notions of set, topological space, topological manifold, smooth manifold, Riemannian manifold, Lorentzian manifold, History of physics and geometry, Introduction to Aristotelian physics
Lecture 3 (09.03.2026): Status of science and philosophy during the era of Aristotle, Aristotelian spacetime, Aristotelian laws of motion, Aristotelian universe model, Heliocentric universe model
Lecture 4 (16.03.2026): Galilean principle of relativity, Newton principle of determinacy, Galilean spacetime, Affine spaces, Galilean boosts, transformations and group, Motion, Newton's laws of motion and gravitation, Kinetic and potential energy, Lagrangian and Hamiltonian formulations of classical mechanics, Poisson bracket and Lie algebras
Lecture 5 (23.03.2026): History of electricity, magnetism and light, Aether theories, Electric and magnetic fields, Maxwell equations, Lorentz transformations, Poincare group, Minkowski spacetime, Einstein's special relativity, Relativity of simultaneity, Light cone and causal structures, Velocity addition formula, Time dilation, Length contraction, Energy formula, Classical limit, İnönü-Wigner contraction
Lecture 6 (30.03.2026): Equivalence principle, Gravity and acceleration, Diffeomorphism invariance, Need for curved spacetimes, Smooth manifolds, Smooth maps, Rings of smooth functions, Tangent bundle, Vector fields, Derivations, Cotangent bundle, 1-forms, Tensors
Lecture 7 (06.04.2026): Vector fields, Lie bracket, Lie algebras and Lie algebroids, 1-forms, Tensors, Metrics, Cartan calculus: Exterior derivative, Lie derivative, Interior product, Cartan relations, Affine connections, Torsion, Curvature, Non-metricity
Lecture 8 (20.04.2026): Affine connections, Parallel transport, Torsion, Curvature, Non-metricity tensors, Fundamental theorem of Riemannian geometry, Koszul formula, Schouten decomposition, Classification of metric-affine geometries, Ricci tensor, Ricci scalar, Einstein tensor, Einstein field equations
Lecture 9 (27.04.2026): Ricci tensor, Ricci scalar, Einstein tensor, Einstein field equations, Calculations of a local frame: connection, anholonomy, Levi-Civita coefficients, components of torsion, curvature, non-metricity tensors
Lecture 10 (04.05.2026): Cosmological solutions, FLWR metric, Black hole solutions, Schwarzchild metric
Lecture 11 (11.05.2026): Discussion on JacoPy engine details
Lecture 12 (18.05.2026): Algebroids, Lie algebroids, Courant algebroids, Hierarchy of algebroids, Metric-affine geometry on algebroids, Torsion, Curvature, Non-metricity, Locality operator and locality projector, Modified and projected modified torsion and curvature, Closing remarks on general relativity on algebroids, Courant sigma model, Quantum mechanics, Standard model, Quantum gravity and String theory