These lectures were given to third-year mathematics undergraduates at Oxford in the late 1970s and early 1980s. The notes were produced originally in mimeographed form by the Mathematical Institute at Oxford in 1977, and in a revised edition in 1980. I have made further minor changes and corrections in this edition, and added some examples and exercises from problem sheets given out in lectures by Roger Penrose and Paul Tod. Special relativity provides one of the more interesting pedagogical challenges. This particular course was given to students with a strong mathematical background who...