A key goal of the first set of lectures is to introduce the L2 theory of Hormander and as an application to solve the Levi problem.
A discussion of current research problems in function theory of several complex variables will complement the introductory material.
John Erik Fornaess,
University of Michigan and
Norwegian University of Science
Textbook: An Introduction to Complex Analysis in Several Variables, L. Hormander (1966).
Fornaess' Beijing lectures (here).
Fornaess' notes for the current school (here).