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Table of Contents

0. Preliminaries.- §1. Abelian Categories.- §2. Homological Algebra in Abelian Categories.- §3. Inductive Limits.- I. Topologies and Sheaves.- §1. Topologies.- §2. Abelian Presheaves on Topologies.- §3. Abelian,Sheaves on Topologies.- II. Étale Cohomology.- §1. The Étale Site of a Scheme.- §2. The Case X= spec(k).- §3. Examples of Étale Sheaves.- §4. The Theories of Artin-Schreier and of Kummer.- §5. Stalks of Étale Sheaves.- §6. Strict Localizations.- §7. The Artin Spectral Sequence.- §8. The Decomposition Theorem. Relative Cohomology.- §9. Torsion Sheaves, Locally Constant Sheaves, Constructible Sheaves.- §10. Étale Cohomology of Curves.- §11. General Theorems in Étale Cohomology Theory.