In recent technical literature more and more of often one comes across such terms as "topology of a molecule", " topological properties", "topological bonding", etc. Broadly speaking, topology is a branch of mathematics dealing with the phenomenon of continuity. A more detailed definition would require from the reader a more profound knowledge of many complex mathematical concepts. This book, however, is designed primarily for a chemist. Besides, it is a popular science book (of course, if one regards as popular science not only books of what chemistry makes of timber type). For this reason we shall give here only the most essential data on topology. Some ten years ago only the few were aware of the existence of molecules without chemical bonds. Nowadays a new scientific discipline, chemical topology, appeared to study them. This science has succeeded in predicting and producing many remarkable chemical compounds (e.g. catenanes whose molecules are interconnected like links of a chain), in defining the electronic structure of molecules more precisely, and so on. The complicated concepts of chemical topology are presented here in a clear and comprehensible form. The booklet is intended for teachers and university and high-school students majoring in chemistry and mathematics. The book was translated from the Russian by Yuri Atanov and was first published by Mir Publishers in 1981.