Review of the uses of invariants in special relativity -- Accelerated motion in special relativity -- Realizations of continuous groups -- Riemannian manifolds -- The free particles. Geodesics -- Weak field approximation. Newton's theory -- Ensembles of particles -- Production of gravitational fields by matter -- Conservation laws -- Phenomenological description of a conservative continuous medium -- Solubility of the Einstein and matter equations -- Energy, momentum and stress in the gravitational field -- Measurement of asymptotic fields -- The electromagnetic field -- Gravitational waves -- Appendix A: Spinning bodies -- Appendix B: Weak field gravitational wave -- Appendix C: Stationary spherically )or rotationally( symmetric metric -- Appendix D: Kerr metric subcalculations -- Appendix E: Friedmann cosmology -- Appendix F: Dynamical equations and diffeomorphisms