The mathematical formulation of the very basic physical principles constitutes the guideline of this course. The principle of relativity, the use of symmetries and covariance, the equivalence principle and the cosmological principle are successively used to arrive at the modern formulation of gravitation in a fully covariant way. The course restarts from very basic newtonian physics and electromagnetism to special and general relativity. At each step, a special attention is paid on the generalisation of the mathematical tools required to formulate the underlying physical idea. This approach leads students to progressively leave their elementary knowledge of basic geometry and differential calculus for adopting the powerful tools of pseudo-riemaniann geometry. The course also illustrate how this approach has been widely acknowledged through an impressive amount of experimental verifications. A similar reasoning on the cosmological principle is used to introduce the modern theory of cosmic expansion and Friedmann-Lemaître universes. Finally, part of the course is devoted to current questions and hot topics, depending on the audience and undergoing researches.
