Nicolas Bourbaki - Books By Bourbaki

Books By Bourbaki

Aiming at a completely self-contained treatment of the core areas of modern mathematics based on set theory, the group produced the Elements of Mathematics (Éléments de mathématique) series, which contains the following volumes (with the original French titles in parentheses):

1. Set theory (Théorie des ensembles)
2. Algebra (Algèbre)
3. Topology (Topologie générale)
4. Functions of one real variable (Fonctions d'une variable réelle)
5. Topological vector spaces (Espaces vectoriels topologiques)
6. Integration (Intégration)

and later

7. Commutative algebra (Algèbre commutative)
8. Lie theory (Groupes et algèbres de Lie)
9. Spectral theory (Théories spectrales)

The book Variétés différentielles et analytiques was a fascicule de résultats, that is, a summary of results, on the theory of manifolds, rather than a worked-out exposition. A final volume IX on spectral theory (Théories spectrales) from 1983 marked the presumed end of the publishing project; but a further commutative algebra fascicle was produced in 1998.