Textbook in PDF format

This book presents basic General Relativity and provides a basis for understanding and using the fundamental theory. General Relativity is a beautiful geometric theory, simple in its mathematical formulation. It leads to numerous consequences with striking physical interpretations: gravitational waves, black holes, cosmological models, and so on. The first part of the book outlines the fundamentals of the subject. Chapters in this part look at Riemannian and Lorentzian geometry, Special and General Relativity, the Einstein equations, the Schwarzschild spacetime, black holes, and cosmology. The second part presents a number of more advanced topics such as general Einstein spacetimes, the Cauchy problem, relativistic fluids, and Relativistic Kinetic Theory.
Fundamentals
Riemannian and Lorentzian Geometry
Special Relativity
General Relativity
The Einstein equations
The Schwarzschild spacetime
Black holes
Introduction to cosmology
Advanced Topics
General Einsteinian spacetimes. The Cauchy problem
Relativistic fluids
Relativistic Kinetic Theory