This is a survey article concerning complex analysis, mostly in several complex variables. After introducing some notation, the author discusses in sections 2 and 3 domains of holomorphy, the notion of holomorphic convexity, and Hartogs extension theorem. Section 4 deals with the classification of domains, starting in one variable with Riemann's mapping theorem, and then with Poincaré's theorem to the effect that in complex dimension already greater than one, the ball and the bidisc are not biholomorphic. A more detailed analysis of biholomorphic equivalence in several variables is given in terms of CR-structures on the boundary, including \textit{C. Fefferman}'s theorem in [Invent. Math. 26, 1-65 (1974; Zbl 0289.32012)], and the theorem of \textit{S. Bell} and \textit{E. Ligocka} [Invent. Math. 57, 283-289 (1980; Zbl 0421.32015)]. The rest of section 4 is devoted to discussing various aspects of the \(\overline{\partial}\)-Neuman problem, its relation to the Bergman projection, and subelliptic estimates.