Several complex variables is a well-established common name for function theory?/analytic geometry/potential theory in several complex variables, i.e. the study of complex manifolds of finite even dimension as well as some generalizations like complex space?s.
The study of several complex variables is qualitatively much different from the theory of functions of one complex variable: for example, natural (inextendable) domains of holomorphy are not at all what one might guess based on the one-variable case (Hartogs lemma?), and similarly for the question of when two domains are biholomorphic. More subtle geometric conditions such as pseudoconvexity? come to the fore.