Textbook in PDF format

Preface to the Polish Edition
Preface to the English Edition
Preliminarios: algebra
Rings, fields, modules, ideals, vector spaces
Polynomials
Polynomial mappings
Symmetric polynomials. Discriminant
Extensions of fields
Factorial rings
Primitive element theorem
Extensions of rings
Noetherian rings
Local rings
Localization
Krull's dimension
Modules of syzygies and homological dimension
The depth of a module
Regular rings
Topology
Some topological properties of sets and families of sets
Open, closed and proper rnappings
Local homeomorphisms and coverings
Germs of sets and functions
The topology of a finite dimension al vector space (over C or R)
The topology of the Grassmann space
Complex analysis
Holomorphic mappings
The Weierstrass preparation theorem
Complex manifolds
The rank theorem. Submersions
Rings of germs of holomorphic functions
Elementary properties. Noether and local properties. Regularity
Unique factorization property
The Preparation Theorem in Thom-Martinet version
Analytic sets, analytic germs and their ideals
Dimension
Thin sets
Analytic sets and germs
Ideals of germs and the loci of ideals. Decomposition into simple germs
Principal germs
One-dimensional germs. The Puiseux theorem
Fundamental lemmas
Lemmas on quasi-covers
Regular and k-normal ideals and germs
Rückert's descriptive lemma
Hilbert's Nullstellensatz and other consequences (concerning dimension, regularity and k-normality)
Geometry of analytic sets
Normal triples
Regular and singular points. Decomposition into simple components
Some properties of analytic germs and sets
The ring of an analytic germ. Zariski's dimension
The maximum principle
The Remmert-Stein removable singularity theorem
Regular separation
Analytically constructible sets
Holomorphic mappings
Some properties of holomorphic mappings of manifolds
The multiplicity theorem. Rouché's theorem
Holomorphic mappings of analytic sets
Analytic spaces
Remmert's proper mapping theorem
Remmert's open mapping theorem
Finite holomorphic mappings
c-holomorphic mappings
Normalization
The Cartan and Oka coherence theorems
Normal spaces. Universal denominators
Normal points of analytic spaces
Normalization
Analyticity and algebraicity
Algebraic sets and their ideals
The projective space as a manifold
The projective closure of a vector space
Grassmann manifolds
Blowings-up
Algebraic sets in projective spaces. Chow's theorem
The Rudin and Sadullaev theorems
Constructible sets. The Chevalley theorem
Rückert's lemma for algebraic sets
Hilbert's Nullstellensatz for polynomials
Further properties of algebraic sets. Principal varieties. Degree
The ring of an algebraic subset of a vedor space
Bézout's theorem. Biholomorphic mappings of projective spaces
Meromorphic functions and rational functions
Ideals of O_n with polynomial generators
Serre's algebraic graph theorem
Algebraic spaces
Biholomorphic mappings of factorial subsets in projective spaces
The Andreotti-Salmon theorem
Chow's theorem on biholomorphic mappings of Grassmann manifolds
References
Notation index
Subject index