Elements of General Relativity Introduction to tensor calculus and Riemannian geometry Curved space time The Schwarzschild metric Weak fields gravitational waves Stars Cosmology. This book provides an introduction to the mathematics and physics of general relativity its basic physical concepts its observational implications and the new insights obtained into the nature of space time and the structure of the universe. It introduces some of the most striking aspects of Einsteins theory of gravitation: black holes gravitational waves stellar models and cosmology. It contains a self contained introduction to tensor calculus and Riemannian geometry using in parallel the language of modern differential geometry and the coordinate notation more familiar to physicists. The author has strived to achieve mathematical rigour with all notions given careful mathematical meaning while trying to maintain the formalism to the minimum fit for purpose. Familiarity with special relativity is assumed. The overall aim is to convey some of the main physical and geometrical properties of Einsteins theory of gravitation providing a solid entry point to further studies of the mathematics and physics of Einstein equations.