Grauert, Hans The methods of the theory of functions of several complex variables. (English) Zbl 0737.32001 Miscellanea mathematica, Festschr. H. Götze, 129-143 (1991). [For the entire collection see Zbl 0723.00017.]The author describes the development of complex analysis from the beginning of the century to the present time. He begins with the Hartogs figure and then he discusses pseudo-convex domains, the Weierstrass preparation theorem, Cousin problems, coherent sheaves, nonreduced complex spaces, isolated singularities, Moishezon spaces, connections with algebraic geometry, Hodge theory, negative line bundles and many other problems. The article is written with mastership, very clearly, with sketches of some proofs or with indications of the methods used, it is described how problems and notions lead naturally to other ones, for what purpose some methods were introduced. This gives a good idea of complex analysis in general for a non-specialist and every person interested in the subject should read this article! Reviewer: K.Dabrowski (Piastow) Cited in 1 Document MSC: 32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 32Dxx Analytic continuation 32Fxx Geometric convexity in several complex variables 32Hxx Holomorphic mappings and correspondences 32Jxx Compact analytic spaces 32Lxx Holomorphic fiber spaces 01A60 History of mathematics in the 20th century 32Axx Holomorphic functions of several complex variables 32Bxx Local analytic geometry 32Cxx Analytic spaces Keywords:harmonic forms; isolated singularity; hull of holomorphy; pseudoconvex domains; coherent sheaves; nonreduced complex spaces; Moishezon spaces; negative line bundles Citations:Zbl 0723.00017 × Cite Format Result Cite Review PDF