Cet ouvrage est une réédition numérique d'un livre paru au XXe siècle, désormais indisponible dans son format d'origine.

Écrits logiques - Suivis d'une Notice biographique, et d'une Note sur la pensée de Herbrand

Théorie des groupes de Lie (3). Théorèmes généraux sur les algèbres de Lie

Classification des groupes algébriques semi-simples. - The Classification of Semi-simple Algebraic Groups

This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as: the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms.
The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and hornorriorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the correspondinq Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontriagin's duality theorem for Abelian groups.
The continued importance of Lie groups in mathematics and theoretical physics makes this an indispensable volume for researchers in both fields.

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