This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry. Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities.

- Varieties in projective space
- Local properties
- Divisors and differential forms
- Intersection numbers
- Schemes
- Varieties
- Complex algebraic varieties and complex manifolds
- Complex Manifolds
- Uniformisation

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