This is a book of elementary geometric topology in which geometry frequently illustrated
guides calculation. The book starts with a wealth of examples often subtle of how to be
mathematically certain whether two objects are the same from the point of view of topology.
After introducing surfaces such as the Klein bottle the book explores the properties of
polyhedra drawn on these surfaces. Even in the simplest case of spherical polyhedra there are
good questions to be asked. There are many examples and exercises making this a useful textbook
for a first undergraduate course in topology. For much of the book the prerequisites are slight
though so anyone with curiosity and tenacity will be able to enjoy the book. As well as
arousing curiosity the book gives a firm geometrical foundation for further study. A
Topological Aperitif provides a marvellous introduction to the subject with many different
tastes of ideas.Stephen Huggett and David Jordan have excellent credentials for explaining the
beauty of this curiously austere but potentially enormously general form of geometry. Professor
Sir Roger Penrose OM FRS Mathematical Institute Oxford UK
