The complex plane. Functions of a complex variable: the complex derivative, analytic functions. Serie di Taylor. Singularities of an analytic function: poles, essential singularities, Laurent series. The residue theorem, applications. The argument principle, Rouche's theorem, the maximum modulus principle.
Spaces of analytic functions: elements of Functional Analysis, the L^{p}-spaces. The Hardy spaces H^{p}: factorization, interpolation. Connections with H^{infty} control theory.