I Varieties. - II Schemes. - III Cohomology. - IV Curves. - V Surfaces. - Appendix A Intersection Theory. - 1 Intersection Theory. - 2 Properties of the Chow Ring. - 3 Chern Classes. - 4 The Riemann-Roch Theorem. - 5 Complements and Generalizations. - Appendix B Transcendental Methods. - 1 The Associated Complex Analytic Space. - 2 Comparison of the Algebraic and Analytic Categories. - 3 When is a Compact Complex Manifold Algebraic?. - 4 Kähler Manifolds. - 5 The Exponential Sequence. - Appendix C The Weil Conjectures. - 1 The Zeta Function and the Weil Conjectures. - 2 History of Work on the Weil Conjectures. - 3 The /-adic Cohomology. - 4 Cohomological Interpretation of the Weil Conjectures. - Results from Algebra. - Glossary of Notations. Language: English