It is the object of this introduction to give a general survey of the material which faces the student of algebraic topology, and at the same time to give a guide to the sources from which this material can most conveniently be studied. It seems convenient to alternate between passages which comment on the material and passages which comment on the literature. When I have had to comment on a topic which has been treated by several authors, I have sometimes felt a responsibility to offer the student some guidance on which source to try first; I have done this by marking a recommended source with an asterisk. This does not mean that the other sources are not also good; some students may prefer them, and most will profit by seeing the same topic treated from more than one point of view. In some cases the marked source is chosen on the grounds that it gives a particularly short, simple or elementary account, while the others give longer, fuller or more advanced accounts.

In what follows, I shall refer to the following list of sources available in book form. A reference to the authorTs name, without further details, is a reference to this list.

J. F. Adams, ‘stable Homotopy Theory’, J. Springer, 2nd ed. 1966 (Lecture Notes in Mathematics No. 3).

P. Alexandroff and H. Hopf, ‘Topologie’, J. Springer 1935.