One service mathematics has rendered the human race. It has put common sense back where it belongs. It has put common sense back where it belongs on the topmost shelf next to the dusty canister labelled discarded nonsense. Eric TBell Every picture tells a story. Advenisement for for Sloan s backache and kidney oils 1907 The book you have in your hands as you are reading this is a text on3-dimensional topology. It can serve as a pretty comprehensive text book on the subject. On the other hand it frequently gets to the frontiers of current research in the topic. If pressed I would initially classify it as a monograph but thanks to the over three hundred illustrations of the geometrical ideas involved as a rather accessible one and hence suitable for advanced classes. The style is somewhat informal; more or less like orally presented lectures and the illustrations more than make up for all the visual aids and handwaving one has at one s command during an actual presentation.