Preliminaries: Holomorphic functions in $C^n$ : definition , the generalized Cauchy integral formula, holomorphic functions: power series development(s), circular and Reinhardt domains, analytic continuation : basic theory and comparisons with the one- variable theory.
Convexity theory: Analytic continuation: the role of convexity, holomorphic convexity, plurisub-harmonic functions, the Levi problem and the role of the d-bar equation.
The d- bar equation: Review of distribution theory, Hormander’s solution and estimates for the d-bar operator.
Suggested books and references:
Lars Hormander, An Introduction to Complex Analysis in Several Variables, 3rd edition, North-Holland Mathematical Library, North-Holland, 1989.
Function Theory of Several Complex Variables, 2nd edition, Wadsworth & Brooks/Cole, 1992.
Raghavan Narasimhan, Several Complex Variables, Chicago Lectures in Mathematics Series, The University of Chicago Press, 1971.