The Texas A&M library subscribes to a collection of Springer books that can be downloaded on campus for free in pdf. (The campus package also allows some of these books to be purchased as hard copies at a significant discount from the list price.) The following items are relevant to this course.

• R. Michael Range, Holomorphic Functions and Integral Representations in Several Complex Variables, 1986, volume 108 in the Graduate Texts in Mathematics series. The first two chapters are an introduction to multidimensional function theory. Then the material becomes more specialized, with an emphasis on integral representations.
• Christine Laurent-Thiébaut, Holomorphic Function Theory in Several Variables: An Introduction, 2011, in the Universitext series. Like the preceding item, this book emphasizes integral representations.
• Volker Scheidemann, Introduction to Complex Analysis in Several Variables, 2005, published under the Birkhäuser imprint. Intended for students, this book is a thin volume with a deliberately restricted scope.
• Klaus Fritzsche and Hans Grauert, From Holomorphic Functions to Complex Manifolds, 2002, volume 213 in the Graduate Texts in Mathematics series. This book is an extensive revision of the authors’ 1976 book, Several Complex Variables, which is volume 38 in the Graduate Texts in Mathematics series. The first two chapters are an introduction to multidimensional function theory. Then the material becomes more specialized, with an emphasis on analysis on manifolds.
• Franc Forstnerič, Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis, 2011, volume 56 in the third series of Ergebnisse der Mathematik und ihrer Grenzgebiete. This advanced book is at the frontiers of research. Chapter 4 is the first textbook treatment of automorphisms of \(\mathbb{C}^n\).
• Walter Rudin, Function Theory in the Unit Ball of \(\mathbb{C}^n\), 2008, in the Classics in Mathematics series, reprint of the 1980 edition (originally published as volume 241 in the Grundlehren der mathematischen Wissenschaften series). In the restricted setting of the unit ball, a lot can be said in detail about function theory.
• Kehe Zhu, Spaces of Holomorphic Functions in the Unit Ball, 2005, volume 226 in the Graduate Texts in Mathematics series. The focus is on the functional-analysis side of the subject in the restricted setting of the unit ball.
• Herbert Alexander and John Wermer, Several Complex Variables and Banach Algebras, third edition, volume 35 in the Graduate Texts in Mathematics series. The book addresses various topics in multidimensional complex analysis from the point of view of Banach algebras.

Here are some relevant non-free books from other publishers.

• Steven G. Krantz, Function Theory of Several Complex Variables, second edition, 1992. This textbook is widely cited. The author has written many other books, some of which have to do with multidimensional complex analysis.
• Robert C. Gunning and Hugo Rossi, Analytic Functions of Several Complex Variables, 1965. Now a bit dated, this is the book from which everybody learned the subject half a century ago. In 1990, the first author published a three-volume update titled Introduction to Holomorphic Functions of Several Variables. As far as I know, these three volumes are not available at a reasonable price, but the campus library holds the first two volumes.
• Lars Hörmander, An Introduction to Complex Analysis in Several Variables, third edition, 1990. This famous book contains an account of Hörmander’s \(L^2\) theory for the ∂ operator.
• So-Chin Chen and Mei-Chi Shaw, Partial Differential Equations in Several Complex Variables, 2001. This book is a comprehensive treatment of the inhomogeneous multidimensional Cauchy–Riemann equations. The second author was a member of the Texas A&M faculty early in her career.
• Emil J. Straube, Lectures on the \(L^2\)-Sobolev Theory of the ∂-Neumann Problem, 2010. This advanced book by a current member of the Texas A&M faculty is at the frontiers of research. A complementary book by Friedrich Haslinger, The ∂ Neumann Problem and Schrödinger Operators, 2014, is available for free online access through the campus library contract with ProQuest Ebook Central.