Volker Scheidemann 
Introduction to Complex Analysis in Several Variables 

The idea for this book came when I was an assistant at the Department of Mat- matics and Computer Science at the Philipps-University Marburg, Germany. S- eraltimes Ifacedthetaskofsupportinglecturesandseminarsoncomplexanalysis of several variables and found out that there are very few books on the subject, compared to the vast amount of literature on function theory of one variable, let alone on real variables or basic algebra. Even fewer books, to my understanding, were written primarily with the student in mind. So it was quite hard to ?nd s- porting examples and exercises that helped the student to become familiar with the fascinating theory of several complex variables. Of course, there are notable exceptions, like the books of R.M. Range [9] or B. and L. Kaup [6], however, even those excellent books have a drawback: they are quite thick and thus quite expensive for a student’s budget. So an additional motivation to write this book was to give a comprehensive introduction to the theory of several complex variables, illustrate it with as many examples as I could ?nd and help the student to get deeper insight by giving lots of exercises, reaching from almost trivial to rather challenging. There are not many illustrations in this book, in fact, there is exactly one, becauseinthetheoryofseveralcomplexvariables I?ndmostofthemeithertrivial or misleading. The readers are of course free to have a di?erent opinion on these matters.

Table of Content

Elementary theory of several complex variables.- Continuation on circular and polycircular domains.- Biholomorphic maps.- Analytic Sets.- Hartogs’ Kugelsatz.- Continuation on Tubular Domains.- Cartan-Thullen Theory.- Local Properties of holomorphic functions.