1. Introduction -- 2. Physics in external gravitational fields -- 3. Einstein's field equations -- 4. The Schwarzschild solution and classical tests of general relativity -- 5. Weak gravitational fields -- 6. The post-Newtonian approximation -- 7. White dwarfs and neutron stars -- 8. Black holes -- 9. The positive mass theorem -- 10. Essential of Friedmann-Lemaãitre models -- 11. Differentiable manifolds -- 12. Tangent vectors, vector and tensor fields -- 13. The lie derivative -- 14. Differential forms -- 15. Affine connections -- 16. Some details and supplements -- Appendix A. Fundamental equations for hypersurfaces -- Appendix B. Ricci curvature of warped products -- Appendix C. Frobenius integrability theorm -- Appendix D. Collection of important formulas.