From Holomorphic Functions to Complex Manifolds

I Holomorphic Functions.- 1. Complex Geometry.- 2. Power Series.- 3. Complex Differentiable Functions.- 4. The Cauchy Integral.- 5. The Hartogs Figure.- 6. The Cauchy-Riemann Equations.- 7. Holomorphic Maps.- 8. Analytic Sets.- II Domains of Holomorphy.- 1. The Continuity Theorem.- 2. Plurisubharmonic Functions.- 3. Pseudoconvexity.- 4. Levi Convex Boundaries.- 5. Holomorphic Convexity.- 7. Examples and Applications.- 8. Riemann Domains over Cn.- 9. The Envelope of Holomorphy.- III Analytic Sets.- 1. The Algebra of Power Series.- 2. The Preparation Theorem.- 3. Prime Factorization.- 4. Branched Coverings.- 5. Irreducible Components.- 6. Regular and Singular Points.- IV Complex Manifolds.- 1. The Complex Structure.- 2. Complex Fiber Bundles.- 3. Cohomology.- 4. Meromorphie Functions and Divisors.- 5. Quotients and Submanifolds.- 6. Branched Riemann Domains.- 7. Modifications and Toric Closures.- V Stein Theory.- 1. Stein Manifolds.- 2. The Levi Form.- 3. Pseudoconvexity.- 4. Cuboids.- 5. Special Coverings.- 6. The Levi Problem.- VI Kahler Manifolds.- 1. Differential Forms.- 2. Dolbeault Theory.- 3. Kähler Metrics.- 4. The Inner Product.- 5. Hodge Decomposition.- 6. Hodge Manifolds.- 7. Applications.- VII Boundary Behavior.- 1. Strongly Pseudoconvex Manifolds.- 2. Subelliptic Estimates.- 3. Nebenhüllen.- 4. Boundary Behavior of Biholomorphic Maps.- References.- Index of Notation.