Analytic continuation, domains and envelopes of holomorphy. The Cousin problems. Introduction to integral formulas in several variables and their applications, e.g., to the solution of -problems. The notion of complex manifolds. Some of the simplest notions from the local theory of holomorphic functions and varieties. Introduction to sheaf theory and sheaf cohomology. Applications of sheaf-theoretic methods in complex analysis. CR-manifolds and CR-functions. Approximation theorems. Topics in the boundary behavior of holomorphic functions. Other topics as time permits and interests suggest.

Sources: No text is required. Good references are the following:

• R. C. Gunning, Introduction to Holomorphic Functions of Several Complex Variables (three volumes).
• L. V. Hörmander, Complex Analysis in Several Variables.
• E. M. Chirka, Complex Analytic Sets.
• R. M. Range, Holomorphic Functions and Integral Representations in Several Complex Variables.

Prerequisites: An introduction to function theory in one complex variable.  Stokes's theorem in the setting of manifolds.