This unusual book, richly illustrated with 19 colour platesand about 250 line drawings, explores the relationshipbetween classical tessellations and3-manifolds. In hisoriginal entertaining style with numerous exercises andproblems, the author provides graduate students with asource of geomerical insight to low-dimensional topology, while researchers in this field will find here an account ofa theory that is on the one hand known tothem but here ispresented in a very different framework.