Introduction to general relativity, black holes, and cosmology / Yvonne Choquet-Bruhat, with a foreword by Thibault Damour.

Includes bibliographical references (pages 267-272) and index.

Part A: Fundamentals -- Riemannian and Lorentzian geometry -- Special relativity -- General relativity -- The Einstein equations -- The Schwarzschild spacetime -- Black holes -- Introduction to cosmology -- Part B: Advanced topics -- General Einsteinian spacetimes -- Relativistic fluids -- Relativistic kinetic theory.

General Relativity is a beautiful geometric theory, simple in its mathematical formulation but leading to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. This introductory textbook is written for mathematics students interested in physics and physics students interested in exact mathematical formulations (or for anyone with a scientific mind who is curious to know more of the world we live in), recent remarkable experimental and observational results which confirm the theory are clearly described and no specialised physics knowledge is required. The mathematical level of Part A is aimed at undergraduate students and could be the basis for a course on General Relativity. Part B is more advanced, but still does not require sophisticated mathematics.