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Preface 1. Algebraic Foundations 2. Algebraic Varieties: Fundamental Concepts 3. Transformations of Algebraic Varieties 4. Formal Power Series 5. Algebraic Curves, Their Places and Transformations 6. Linear Series 7. Abelian Differentials 8. Abel’s Theorem. Algebraic Series and Correspondences 9. Systems of Curves on a Surface Appendix Bibliography List of symbols most frequently used in the text Index