This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.

‘This book achieves the purpose of providing an introduction which reaches the developing parts of the subject, and for those who already know a little algebraic topology is by far the best textbook for further study.’

Source: D.G. Palmer in Proceedings of the Edinburgh Mathematical Society

‘This is a badly needed book. It does an excellent job of carrying the serious beginning student of algebraic topology to a genuine acquaintance with the field.’

Source: A. Heller in American Mathematical Reviews

‘The book is written with great skill and contains a large number of exercises. The authors constantly emphasise the geometrical nature of the ideas they examine’.

P.S. Alexandrov in the Preface to the Russian edition