The Association of Collaborators of Nicolas Bourbaki (l'Association des collaborateurs de Nicolas Bourbaki) is a group of mathematics in France who set the standard for a structural and abstract approach to exposition of pure mathematics in the 20th century. They published a series “Elements of mathematics” of 10 multi-volume monographs under the pseudonym ‘Nicolas Bourbaki’, consolidating known results. They also held —and still hold— a largely independent seminar on contemporary research.
The members of the group at any one time are required to be under 50 years of age, which is considered the only fixed rule of the group; the membership is taken under acceptance of an invitation by existing members. For a bit of history can be found at en.wikipedia, fr.wikipedia, britannica and references therein.
According to Jean Dieudonné, Bourbaki exposition is dedicated to dead and stable mathematics which is not likely to change soon and which has wider importance, rather than being of a specialized character. Most successful was the exposition of the chapters on Lie theory, especially Lie algebras, whose style is later followed in much of later literature in the subject. See more in
Mathematically, the biggest single credit to Bourbaki is for decisively defining a general notion of structure (which was largely as a formal scope of mainstream mathematics in the second half of 20th century). Bourbaki is blamed for too formal approach; indeed books are void of much motivation and application, apart from a few of introductions and few chapters on history. Bourbaki unfortunately did not embrace category theory, though some of the universal properties treated in category theory in fact first appeared in early editions of Bourbaki. Apart from Bourbaki volumes, there is also a lively Bourbaki seminar which takes place on certain Saturdays in Paris, is open to public, has non-Bourbaki members as invited speakers who present and discuss in advance chosen topics of recent development in mathematics; the expositions are subsequently published.
Bourbaki’s biography at math tutor: the pre-war years, the after-war years
website of the group
Amir D. Aczel, The artist and the mathematician: the story of Nicolas Bourbaki, the genius mathematician who never existed, Thunder’s Mouth Press, New York, 2006, viii+239 pp. MR2008h:01020, SIAM review