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Théorie des groupes de Lie. Groupes algébriques. Théorèmes généraux sur les algèbres de Lie. 2ième éd. (French) Zbl 0186.33104
Publications de l’Institut de Mathématique de l’Université de Nancago. I et IV. Paris: Hermann & Cie. ix, 418 p. (1968).
The present book is the second edition of the author’s book: Théorie des groupes de Lie. Tome II. Groupes algébriques; and Tome III. Théorèmes généraux sur les algèbres de Lie, which have been published in 1951 and 1955 in the collection of Actuarités Scientifiques et Industrielles. 1152 (1951; Zbl 0054.01303) and 1226 (1955) and form also volumes I and IV of the “Publications de l’Institut Mathématique de l’Universite de Nancago”, respectively. They are now bound together in one volume and reproduce the original volumes in full.
Since these volumes have first been published, the theory of algebraic groups has made many remarkable developments by the author, A. Borel and others with the aid of the theory of algebraic geometry. In this direction, recently, we have a book written by A. Borel, Linear algebraic groups. New York etc.: W. A. Benjamin (1969; see the following review Zbl 0186.33201) which is providing a nice introduction to the theory of linear algebraic groups over fields based on the theory of algebraic geometry. But, if we restrict our attention to those over fields of characteristic 0 (for example, fields of algebraic numbers), the theory based on Lie algebras is commonly useful and rather more elementary than the general theory.
This book is a good “self-contained” introduction to the theory of linear algebraic groups and their Lie algebras and it is valuable even now for those who study linear algebraic groups.

MSC:
22-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to topological groups
20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory
17-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras
14-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry
22Exx Lie groups
20Gxx Linear algebraic groups and related topics
17Bxx Lie algebras and Lie superalgebras
14Lxx Algebraic groups