This book gives a nice introduction to some parts of the theory of several complex variables. It concentrates on a study of the properties of a special class of domains called Reinhardt domains.

Some basic notions in the theory (domains of holomorphy, holomorphic convexity, pseudoconvexity) can be nicely introduced and studied in the setting of Reinhardt domains without too many technical details. In the first chapter of the book, the authors present such an introduction to problems arising in connection to the holomorphic continuation of holomorphic functions in several complex variables. Biholomorphisms of domains and the Cartan theory in the setting of Reinhardt domains are treated in the second chapter. A short third chapter contains a discussion of S-domains of holomorphy for various special classes S of holomorphic functions. The last chapter is devoted to a study of holomorphically contractible families on Reinhardt domains and it includes a lot of explicit calculations in specific cases. Many results presented in the book are based on research by both authors.

Reviewer:

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