This is an introductory textbook on applications of general relativity to astrophysics and cosmology. The aim is to provide graduate students with a toolkit for understanding astronomical phenomena that involve velocities close to that of light or intense gravitational fields. The approach taken is first to give the reader a thorough grounding in special relativity, with space-time the central concept, following which general relativity presents few conceptual difficulties. Examples of relativistic gravitation in action are drawn from the astrophysical domain. The book can be read on two levels: first as an introductory fast-track course, and then as a detailed course reinforced by problems which illuminate technical examples. The book has extensive links to the literature of relativistic astrophysics and cosmology.