André Weil’s mathematical work has deeply influenced the mathematics of the twentieth century. Part of a three-volume set, this work collects his papers in chronological order and includes lengthy commentaries on many of the articles written by Weil himself.

This systematic and self-contained treatment examines the topology of differentiable manifolds, curvature and homology of Riemannian manifolds, compact Lie groups, complex manifolds, and curvature and homology of Kaehler manifolds. It generalizes the theory of Riemann surfaces to that of Riemannian manifolds. Includes four helpful appendixes. "A valuable survey." — Nature. 1962 edition.

Preliminary Material /Henri Clavier -- Introduction Générale /Henri Clavier -- Introduction /Henri Clavier -- Quelques survivances archaïques dans les courants de la pensée biblique /Henri Clavier -- Le courant mystique et la pensée mystique. /Henri Clavier -- Le eourant prophétique dans la pensée biblique /Henri Clavier -- Le courant cultuel et la pensée biblique /Henri Clavier -- Introduction /Henri Clavier -- y A-t-il unité de pensée dans la Bible juive? /Henri Clavier -- Y A-t-il unité de pensée dsns le Nouveau Testament? /Henri Clavier -- Comment y aurait-il unité de pensée d'un Testament A L'autre ? /Henri Clavier -- L'unité au but et l'unité au centre /Henri Clavier -- Conclusion /Henri Clavier -- Index des citations bibliques /Henri Clavier -- Index des noms de lieux /Henri Clavier -- Index des noms de personnes /Henri Clavier -- Index des noms d'auteurs /Henri Clavier -- Table analytique /Henri Clavier.

This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.