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 of coord in ate-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. 1 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. There are enough good ones
in print already. The notes are more or less as I originally wrote them to supplement
the lectures. They clearly owe much to other books, notably those by Bondi1, Rindler2,
and Synge3. It is difficult after so many years to track down all the original sources,
particularly when it comes to problems, which are oftened borrowed from textbooks
and set anonymously as examination questions. I hope that I will be forgiven for not
acknowledging in detail ideas that are part of the common currency of the subject. Many
of the exercises were set in the Mathematics Final Honour School at Oxford.