This highly original work, written by the creators of the multivariable theory of automorphisms, is a rich tapestry of themes and concepts, and a comprehensive treatment of an important area of mathematics. From Poincare's work on biholomorphic inequivalence in 1906, it became clear that the structures of the automorphism groups of domains in multi-dimensional complex space are more complex, and more interesting, than those in the complex plane. The authors build on this theme and trace the evolution of the classical theory to the modern theory, which is today a cornerstone of geometric...