This book has grown out of notes on lecture courses which we have given on projective planes and related topics. It has two main aims: to provide an elementary treatment of the subject, suitable for advanced undergraduates, and yet to give enough insight into the research areas that it may also be used for postgraduate courses. The subject matter is such that there are virtually no mathematical prerequisites for studying many of the earlier chapters, although a maturity in the basic concepts of modern algebra is often an advantage.