'One of the most attractive features of the book is the detailed discussion of discrete analogues of isothermic surfaces and orthogonal systems which were intensively studied in the last decade ... The reviewed monograph will be of great interest for researchers specializing in differential geometry, geometric theory of integrable systems and other related fields.' Zentralblatt MATH 'The book is a well-written survey of classical results from a new point of view and a nice textbook for a study of the subject.' EMS Newsletter 'This book is a work of scholarship, communicating the author's enthusiasm for Mobius geometry very clearly. The book will serve as an introduction to Mobius geometry to newcomers, and as a very useful reference for research workers in the field.' Tom Willmore, University of Durham