Some integral formulas. Subharmonicity and its applications. Convexity. Hormander's solution of the equation. Solution of the Levi problem and other applications of techniques. Cousin problems, cohomology and sheaves. The zero set of a holomorphic function. Some harmonic analysis. Integral formulas for solutions to the problem and norm estimates. Holomorphic mappings and invariant metrics. Constructive methods. Finite type.