General relativity is one of the cornerstones of classical physics, providing a synthesis of special relativity and gravitation, and is central to our understanding of many areas of astrophysics and cosmology. This book is intended to give an introduction to this important subject, suitable for a one-term course for advanced undergraduate or beginning graduate students in physics or in related disciplines such as astrophysics and applied mathematics. Some of the later chapters should also provide a useful reference for professionals in the fields of astrophysics and cosmology.

It is assumed that the reader has already been exposed to special relativity and Newtonian gravitation at a level typical of early-stage university physics courses. Nevertheless, a summary of special relativity from first principles is given in Chapter 1, and a brief discussion of Newtonian gravity is presented in Chapter 7. No previous experience of 4-vector methods is assumed. Some background in electromagnetism will prove useful, as will some experience of standard vector calculus methods in three-dimensional Euclidean space. The overall level of mathematical expertise assumed is that of a typical university mathematical methods course.

The book begins with a review of the basic concepts underlying special relativity in Chapter 1. The subject is introduced in a way that encourages from the outset a geometrical and transparently four-dimensional viewpoint, which lays the conceptual foundations for discussion of the more complicated spacetime geometries encountered later in general relativity.