1 Complex Tori -- 1 Homomorphisms of Complex Tori -- 2 Line Bundles -- 3 The Nรฉron-Severi Group -- 4 The Dual Complex Torus -- 5 Extensions of Complex Tori -- 6 Complementary Subtori and Shafarevich Extensions -- 7 Simple and Indecomposable Complex Tori -- 8 The Endomorphism Algebra of a Complex Torus -- 9 The Theorem of Oort and Zarhin -- 10 The Space of all Complex Tori of Dimension g -- 2 Nondegenerate Complex Tori -- 1 Polarizations of Index k -- 2 Moduli Spaces of Nondegenerate Complex Tori -- 3 The Rosati Involution -- 4 The Dual Polarization -- 5 Poincarรฉโ{128}{153}s Reducibility Theorem for Nongenerate Complex Tori -- 6 The Algebraic Dimension -- 7 Picard Number and Algebraic Dimension of Complex Tori of Dimension 2 -- 3 Embeddings into Projective Space -- 1 Kรคhler Theory of Line Bundles on Complex Tori -- 2 Harmonic Forms with Values in a Nondegenerate Line Bundle -- 3 Maps Associated to a Nondegenerate Line Bundle -- 4 The Family of Abelian Varieties Associated to a Nondegenerate Complex Torus -- 5 Some Properties of the Diffeomeorphism ?v_: X ? Xv_ -- 6 The Rational C?-map ?L,V_: X ? ?N -- 4 Intermediate Jacobians -- 1 Primitive Cohomology of Kรคhler Manifolds -- 2 The Griffiths Intermediate Jacobian -- 3 Some Properties of the Griffiths Intermediate Jacobian -- 4 The Weil Intermediate Jacobian -- 5 The Lazzeri Intermediate Jacobian -- 6 The Abelian Variety Associated to the Griffiths Intermediate Jacobian -- 5 Families of Complex Tori -- 1 Complex Tori with Endomorphism Structure -- 2 The Index of a Complex Torus with Endomorphism Structure -- 3 Complex Tori with Endomorphism Structure of Type Ia -- 4 Complex Tori with Endomorphism Structure of Type Ib -- 5 Complex Tori with Endomorphism Structure of Type II -- 6 The Parameter Spaces of Complex Tori with Endomorphism Structure -- 1 The Space Hg,k -- 2 The Space Km -- 3 The Space Lm,j -- 4 The Space Mm,k -- 5 The Space Nm,k -- 6 The Space Rm,j -- 7 The Space Sn -- 8 The Space Tn -- 9 The Space U(p,q),j -- 10 The Space Vp,q -- 7 Moduli Spaces -- 1 Moduli Problems -- 2 Homogeneous Spaces with Noncompact Stabilizer -- 3 The Moduli Space of all Complex Tori -- 4 Moduli Spaces of Nondegenerate Complex Tori -- 5 Moduli Spaces of Nondegenerate Complex Tori with Endomorphism Structure -- A The Kronecker Product -- B Anti-Involutions on R-Algebras -- C Complex Structures -- References -- Glossary of Notations