It is named after Nicolas Bourbaki, a pseudonymous group of French and other mathematicians of variable membership.
1948/49 through 1964/65 were published as Textes des conférences / Séminaire Bourbaki by the Secrétariat Mathématique, Université Paris.
In 1966, W. A. Benjamin, Inc. issued a special twelve-volume facsimile reproduction of the Séminaire Bourbaki, 1948-1965.
Springer-Verlag published 1968/69 through 1980/81 as part of its Lecture Notes in Mathematics series.
1981/82 to date are published by the Société Mathématique de France as part of Astérisque.