I really expected more from such a title and such an author (group of authors as a matter of fact). The book does not cover the history of all important branches of modern mathematics, and those included are not treated in a complete manner. Their major lacks occur in 20th century mathematics. There's a lot of topics and names missing, for example: algebraic geometry, coding theory, dynamical systems, harmonic analysis, complex analysis, multidimensional complex analysis, hypercomplex analysis, approximation theory,... ; Samuel Eilenberg, Norman Steenrod, Salomon Lefschetz, Elias Stein, Alberto Calderón, Peter Lax, Abraham Besicovitch, Michael Atiyah, Wendell Fleming, Witold Hurewicz...

Eventhough the Bourbaki group has made a great effort to synthesize and standarize a lot of branches of modern mathematics the actual product of their work (the Elements of Mathematics, the Fascicules of Results, etc.) may well become obsolete and forgotten because of their limited perspective. Nevertheless, the book contains some useful data that will prove valuable to those interested in mathematics' history, above all, the first essay on the foundations of mathematics.

Contents: Foundations of Mathematics, Logic, Set Theory; Notation, Combinatorial Analysis; The Evolution of Algebra; Linear Algebra and Multilinear Algebra; Polynomials and Commutative Fields; Divisibility, Ordered Fields; Commutative Algebra, Algebraic Number Theory; Non-Commutative Algebra; Quadratic Forms, Elementary Geometry; Topological Spaces; Uniform Spaces; Real Numbers; Exponentials and Logarithms; n-Dimensional Spaces; Complex Numbers, Measurement of Angles; Metric Spaces; Infinitesimal Calculus; Asymptotic Expansions; The Gamma Function; Function Spaces; Topological Vector Spaces; Integration in Locally Compact Spaces; Haar Measure, Convolution; Integration in Non-Locally Compact Spaces; Lie Groups and Lie Algebras; Groups Generated by Reflections; Root Systems.

Extensive references (not common in Bourbaki writings); nice softbound.