Although I hope this book may be useful to others, I wrote it for students to read either before or after attending the appropriate lectures. For this reason, I have tried to move as rapidly as possible to the points of difficulty, show why they are points of difficulty and explain clearly how they are overcome. If you understand the hardest part of a course then, almost automatically, you will understand the easiest. The converse is not true.
In order to concentrate on the main matter in hand, some of the simpler arguments have been relegated to exercises. The student reading this book before taking the appropriate course may take these results on trust and concentrate on the central arguments which are given in detail. The student reading this book after taking the appropriate course should have no difficulty with these minor matters and can also concentrate on the central arguments. I think that doing at least some of the exercises will help students to 'internalise' the material but I hope that even students who skip most of the exercises can profit from the rest of the book.
I have included further exercises in Appendix K. Some are standard, some form commentaries on the main text and others have been taken or adapted from the Cambridge mathematics exams. None are just 'makeweights', they are all intended to have some point of interest. I have tried to keep to standard notations but a couple of notational points are mentioned in the index under the heading notation.
I have not tried to strip the subject down to its bare bones. A skeleton is meaningless unless one has some idea of the being it supports and that being in turn gains much of its significance from its interaction with other beings, both of its own species and of other species. For this reason, I have included several sections marked by а Ф. These contain material which is not necessary to the main argument but which sheds light on it. Ideally, the student should read them but not study them with anything like the same attention which she devotes to the unmarked sections. There are two sections marked 99 which contain some, very simple, philosophical discussion. It is entirely intentional that removing the appendices and the sections marked with а Ф more than halves the length of the book.