The book introduces the general theory of relativity and includes applications to cosmology. The book contains a thorough introduction to tensor calculus and curved manifolds. After the necessary mathematical tools are introduced, we give a thorough presentation of the theory of relativity. Also, some advanced topics not previously covered by textbooks; e.g. Kaluza-Klein theory, Israel's formalism and branes. Anisotropic cosmological models are also included. The book contains a large number of new exercises and examples, each with separate headings. The reader will get an updated introduction to general relativity including the most recent developments in cosmology.