A topological aperitif 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. More refined tools are developed in a chapter on winding number and an appendix gives a glimpse of knot theory. 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. BOOK JACKET