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 already had a good grounding in classical mathematical physics, but who had not yet met relativity. The emphasis is on the use ofcoordinate-free and tensorial methods: I tried to avoid the traditional arguments based on the standard Lorentz transformation, and to encourage students to look at problems from a four-dimensional point of view. I did not attempt to 'derive' relativity from a minimal set of axioms, but instead concentrated on stating clearly the basic principles and assumptions. Elsewhere in the world, relativity is usually introduced in a more elementary way earlier in undergraduate courses, and even at Oxford, it is now part of the second-year syllabus in mathematics. I doubt, therefore, that anyone would contemplate giving a lecture course exactly along these lines. Nevertheless, I hope that the notes may provide one or two ideas. I have not attempted to produce a polished textbook.