One of the approaches to the study of functions of several complex variables is to use methods originating in real analysis. In this concise book, the author gives a lucid presentation of how these methods produce a variety of global existence theorems in the theory of functions (based on the characterization of holomorphic functions as weak solutions of the CauchyRiemann equations). Emphasis is on recent results, including an \(L^2\) extension theorem for holomorphic functions, that have brought a deeper understanding of pseudoconvexity and plurisubharmonic functions. Based on Oka's theorems and his schema for the grouping of problems, the book covers topics at the intersection of the theory of analytic functions of several variables and mathematical analysis. It is assumed that the reader has a basic knowledge of complex analysis at the undergraduate level. The book would make a fine supplementary text for a graduatelevel course on complex analysis. Readership Graduate students and research mathematicians interested in several complex variables and analytic spaces. Reviews "The goal of this admirable little book is ... to ascend rapidly to a few wellchosen peaks."  Mathematical Reviews "Concise booklet ... The author gives a lucid presentation ... The book would make a fine supplementary text for a graduatelevel course on complex analysis."  Zentralblatt MATH Table of Contents  Holomorphic functions
 Rings of holomorphic functions and \(\overline{\partial}\) cohomology
 Pseudoconvexity and plurisubharmonic functions
 \(L^2\) estimates and existence theorems
 Solutions of the extension and division problems
 Bergman kernels
 Bibliography
 Index
