Complex Analysis deals with properties of holomorphic functions, that is, solutions of the homogeneous Cauchy-Riemann equations. The classical function theory of one variable goes back to Augustin Louis Cauchy and was brought to fruition by Bernhard Riemann; however, it was only realized at the end of the 19th century through the work of Hartogs, Poincaré, and Wirtinger that the theory of several complex variables differs considerably from the one-dimensional case.

Several Complex Variables is closely related to the fields of Partial Differential Equations, Algebraic Geometry, and Functional Analysis; it not only contributes basic tools to those fields but also is influenced deeply by results from them. 

The Complex Analysis group at the University of Vienna is home to researchers interested in a wide variety of topics, both in one-dimensional function theory and several complex variables.