Abelian Varieties

I Algebraic Groups.- 1. Groups, subgroups, and factor groups.- 2. Intersections and Pontrjagin products.- 3. The field of definition of a group variety.- II General Theorems on Abelian Varieties.- 1. Rational maps of varieties into abelian varieties.- 2. The Jacobian variety of a curve.- 3. The Albanese variety.- III The Theorem of the Square.- 1. Algebraic equivalence.- 2. The theorem of the cube and the theorem of the square.- 3. The theorem of the square for groups.- 4. The kernel in the theorem of the square.- IV Divisor Classes on an Abelian Variety.- 1. Applications of the theorem of the square to abelian varieties.- 2. The torsion group.- 3. Numerical equivalence.- 4. The Picard variety of an abelian variety.- V Functorial Formulas.- 1. The transpose of a homomorphism.- 2. A list of formulas and commutative diagrams.- 3. The involutions.- VI The Picard Variety of an Arbitrary Variety.- 1. Construction of the Picard variety.- 2. Divisorial correspondences.- 3. Application to the theory of curves.- 4. Reciprocity and correspondences.- VII The l-Adic Representations.- 1. The l-adic spaces.- 2. Dual representations.- VIII Algebraic Systems of Abelian Varieties.- 1. The K/k-image.- 2. The generic hyperplane section.- 3. The K/k-trace.- 4. The transpose of an exact sequence.- 5. Duality between image and trace.- 6. Exact sequences of varieties.- Appendix Composition of Correspondences.- 1. Inverse images.- 2. Divisorial correspondences.- Table of Notation.