1. Complex Spaces -- ยง 1. The Notion of a Complex Space -- ยง 2. General Properties of Complex Spaces -- ยง 3. Direct Products and Graphs -- ยง 4. Complex Spaces and Cohomology -- 2. Local Weierstrass Theory -- ยง 1. The Weierstrass Theorems -- ยง 2. Algebraic Structure of $${O_{{Ĉn},0}}$$ -- ยง 3. Finite Maps -- ยง4. The Weierstrass Isomorphism -- ยง 5. Coherence of Structure Sheaves -- 3. Finite Holomorphic Maps -- ยง 1. Finite Mapping Theorem -- ยง 2. Rรผckert Nullstellensatz for Coherent Sheaves -- ยง 3. Finite Open Holomorphic Maps -- ยง 4. Local Description of Complex Subspaces in ?n -- 4. Analytic Sets. Coherence of Ideal Sheaves -- ยง 1. Analytic Sets and their Ideal Sheaves -- ยง 2. Coherence of the Sheaves i (A) -- ยง 3. Applications of the Fundamental Theorem and of the Nullstellensatz -- ยง 4. Coherent and Locally Free Sheaves -- 5. Dimension Theory -- ยง 1. Analytic and Algebraic Dimension -- ยง 2. Active Germs and the Active Lemma -- ยง 3. Applications of the Active Lemma -- ยง 4. Dimension and Finite Maps. Pure Dimensional Spaces -- ยง 5. Maximum Principle -- ยง 6. Noether Lemma for Coherent Analytic Sheaves -- 6. Analyticity of the Singular Locus. Normalization of the Structure Sheaf -- ยง 1. Embedding Dimension -- ยง 2. Smooth Points and the Singular Locus -- ยง 3. The Sheaf M of Germs of Meromorphic Functions -- ยง 4. The Normalization Sheaf $${\hat O_X}$$ -- ยง 5. Criterion of Normality. Theorem of Oka -- 7. Riemann Extension Theorem and Analytic Coverings -- ยง 1. Riemann Extension Theorem on Complex Manifolds -- ยง 2. Analytic Coverings -- ยง 3. Theorem of Primitive Element -- ยง 4. Applications of the Theorem of Primitive Element -- ยง 5. Analytically Normal Vector Bundles -- 8. Normalization of Complex Spaces -- ยง 1. One-Sheeted Analytic Coverings -- ยง 2. The Local Existence Theorem. Coherence of the Normalization Sheaf -- ยง 3. The Global Existence Theorem. Existence of Normalization Spaces -- ยง 4. Properties of the Normalization -- 9. Irreducibility and Connectivity. Extension of Analytic Sets -- ยง 1. Irreducible Complex Spaces -- ยง 2. Global Decomposition of Complex Spaces -- ยง 3. Local and Arcwise Connectedness of Complex Spaces -- ยง 4. Removable Singularities of Analytic Sets -- ยง 5. Theorems of Chow, Levi and Hurwitz-Weierstrass -- 10. Direct Image Theorem -- ยง 1. Polydisc Modules -- ยง 2. Proof of Lemmata F(q) and Z(q) -- ยง 3. Sheaves of Polydisc Modules -- ยง 4. Coherence of Direct Image Sheaves -- ยง 5. Regular Families of Compact Complex Manifolds -- ยง 6. Stein Factorization and Applications -- Annex. Theory of Sheaves. Notion of Coherence -- ยง0. Sheaves -- 1. Sheaves and Morphisms โ 2. Restrictions, Subsheaves and Sums of Sheaves โ 3. Sections. Hausdorff Sheaves -- ยง 1. Construction of Sheaves from Presheaves -- 1. Presheaves โ 2. The Sheaf Associated to a Preshaf โ 3. Canonical Presheaves โ 4. Image Sheaves -- ยง 2. Sheaves and Presheaves with Algebraic Structure -- 1. Sheaves of Groups, Rings and A-Modules โ 2. The Category of A-Modules. Quotient Sheaves โ 3. Presheaves with Algebraic Structure โ 4. The Functor Hom โ 5. The Functor ? -- ยง 3. Coherent Sheaves -- 1. Sheaves of Finite Type โ 2. Sheaves of Relation Finite Type โ 3. Coherent Sheaves -- ยง 4. Yoga of Coherent Sheaves -- 1. Three Lemma โ 2. Consequences of the Three Lemma โ 3. Coherence of Trivial Extensions โ 4. Coherence of the Functors Hom and ? โ 5. Annihilator Sheaves -- Index of Names

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