I. A survey of the foundations -- 1. Algebraic varieties -- 2. Absolute and relative varieties -- 3. The local rings -- 4. Algebraic product -- 5. Normal varieties -- 6. Birational transformations -- 7. Simple points -- 8. The intersection multiplicity -- 9. The calculus of cycles -- II. The resolution of singularities -- 1. The local uniformisation theorem -- 2. Monoidal transformations -- 3. Zariski's proof for threefolds -- III. Linear systems -- 1. Divisors -- 2. The definition of linear system -- 3. Linear equivalence -- 4. Complete systems -- 5. The multiples of a linear system -- 6. Ample linear systems -- 7. Bertini's theorems -- IV. The geometric genus -- 1. The adjoint forms -- 2. The canonical system -- 3. The canonical system as a birational invariant -- 4. The arithmetic definition of the canonical system -- 5. Relations between canonical and adjoint systems -- V. The arithmetic genus -- 1. The definition -- 2. The modular property of the arithmetic genus -- 3. The definition of the virtual arithmetic genus of a cycle -- 4. The birational invariance of the arithmetic virtual genus -- 5. The absolute invariance of pa(V) (r ? 3) -- 6. The virtual characters of a cycle -- 7. Virtual and effective dimensions -- 8. A second definition of the arithmetic genus -- 9. The virtual characters of K -- VI. Algebraic and rational equivalence -- 1. The associated variety -- 2. Specialisation of a cycle and algebraic systems -- 3. Algebraic correspondences -- 4. The degeneration principle of Enriques-Zariski -- 5. Fundamental and exceptional varieties -- 6. A property of Chow varieties -- 7. Algebraic equivalence -- 8. Rational equivalence -- 9. The intersection-product for equivalence classes -- 10. A theorem of Severi and its consequences -- VII. The Abelian varieties from the algebraic viewpoint, and related questions -- 1. Jacobi variety -- 2. The base for the group of algebraic equivalence for divisors -- 3. The first Picard variety -- 4. The total maximal algebraic families -- 5. A property of the arithmetic genus -- 6. Non-special total families -- 7. The first Picard variety according to Matsusaka -- 8. The second Picard variety and the superficial irregularity -- VIII. Theory and applications of the canonical systems -- 1. Introduction -- 2. A new definition of the canonical divisors -- 3. Todd's canonical systems -- 4. Introduction to Segre's theory -- 5. The covariant sequence -- 6. The algebra of covariant sequences -- 7. The canonical sequence -- 8. Some applications -- 9. The behaviour of the canonical systems under birational transformations -- 10. Irregular intersection problems -- 11. Miscellaneous results -- IX. The algebraic varieties as complex-analytic manifolds -- 1. The complex manifolds and Chow's theorem -- 2. Hermìte's and Kähler's metrics -- 3. The currents -- 4. The fundamental existence theorems -- 5. The complex operators -- 6. The Hodge-Eckmann theory -- 7. Hodge's birational invariants -- 8. Miscellaneous results -- 9. Chern's classes as canonical classes -- X. The applications of stack theory to algebraic geometry -- 1. Complex line bundles -- 2. The stack concept -- 3. Cohomology groups over a stack -- 4. A theorem of Dolbeault -- 5. Positive complex line bundles -- 6. The Picard variety in stack theory -- 7. The theorem of Riemann-Roch for adjoint systems -- 8. The arithmetic genera -- 9. The Riemann-Roch theorem -- 10. Miscellaneous results -- XI. The superficial irregularity and continuous systems -- 1. The deficiency of a linear system -- 2. The Poincaré families -- 3. The superficial irregularity -- 4. Characteristic systems of complete continuous systems -- 5. Miscellaneous results -- 1. Treatises, Monographs and Reports -- 2. List of papers.