Once the plan of the work was expanded to treat other fields in depth, the title Éléments de mathématique was adopted.

[3][4] A companion volume, Éléments d'histoire des mathématiques (Elements of the History of Mathematics), collects and reproduces several of the historical notes that previously appeared in the work.

In late 1934, a group of mathematicians including André Weil resolved to collectively write a textbook on mathematical analysis.

During the late 1930s and early 1940s, the Bourbaki group expanded the plan of their work beyond analysis, and began publishing texts under the title Éléments de mathématique.

Some early versions of the Éléments can be viewed at an online archive,[14] and the mathematical historian Liliane Beaulieu has documented the sequence of publication.

From the 1940s through the 1960s, Bourbaki published the Éléments in booklet form as small installments of individual chapters, known in the French as fascicules.

Independently of the work's logical structure, the early fascicules were assigned chronological numberings by the publisher Hermann for historical reference.

[15] Gradually, the small fascicules were collected and reprinted in larger volumes, forming the basis of the modern edition of the work.

[16][17][18][a] However, the English General Topology is not based on latest revised French edition (of 1971 and 1974) and misses some material added there (for example on quaternions and rotation groups in Chapter VIII).

The former usually appear after a given chapter to contextualize the development of its topics, and the latter are occasionally used sections in which a book's major results are collected and stated without proof.

When Bourbaki's founders originally planned the Treatise on Analysis, they conceived of an introductory and foundational section of the text, which would describe all prerequisite concepts from scratch.

This portion of the Éléments was gradually realized as its first three books, dealing with set theory, abstract algebra, and general topology.