Nicolas Bourbaki is the collective pseudonym

Pseudonym

A pseudonym is a name that a person assumes for a particular purpose and that differs from his or her original orthonym...

 under which a group of (mainly French

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

) 20th-century mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

s wrote a series of books presenting an exposition of modern advanced mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, beginning in 1935. With the goal of founding all of mathematics on set theory

Set theory

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...

, the group strove for rigour

Rigour

Rigour or rigor has a number of meanings in relation to intellectual life and discourse. These are separate from public and political applications with their suggestion of laws enforced to the letter, or political absolutism...

 and generality. Their work led to the discovery of several concepts and terminologies still discussed.
While Nicolas Bourbaki is an invented personage, the Bourbaki group is officially known as the Association des collaborateurs de Nicolas Bourbaki (Association of Collaborators of Nicolas Bourbaki), which has an office at the École Normale Supérieure

École Normale Supérieure

The École normale supérieure is one of the most prestigious French grandes écoles...

 in Paris

Paris

Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...

.
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
   Set theory
   Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
   
    (Théorie des ensembles)


2. Algebra
   Algebra
   Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
   
    (Algèbre)


3. Topology
   Topology
   Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
   
    (Topologie générale)


4. Functions of one real variable
   Real analysis
   Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the analytic properties of real functions and sequences, including convergence and limits of sequences of real numbers, the calculus of the real...
   
    (Fonctions d'une variable réelle)


5. Topological vector space
   Topological vector space
   In mathematics, a topological vector space is one of the basic structures investigated in functional analysis...
   
   s (Espaces vectoriels topologiques)


6. Integration
   Integral
   Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
   
    (Intégration)

and later

7. Commutative algebra
   Commutative algebra
   Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra...
   
    (Algèbre commutative)


8. Lie theory
   Lie theory
   Lie theory is an area of mathematics, developed initially by Sophus Lie.Early expressions of Lie theory are found in books composed by Lie with Friedrich Engel and Georg Scheffers from 1888 to 1896....
   
    (Groupes et algèbres de Lie)


9. Spectral theory
   Spectral theory
   In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of...
   
    (Théories spectrales)

The book Variétés différentielles et analytiques was a fascicule de résultats, that is, a summary of results, on the theory of manifold

Manifold

In mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....

s, rather than a worked-out exposition.