As far as I understand, each chapter of the Bourbaki's collection was written by one (or two?) specific authors. The book itself was reviewed, corrected and after all approved by the whole Bourbaki assembly (if I may call them this way). But I have the feeling one (or two) specific person was in charge of the writting of any given chapter.
In my opinion, the style and the clarity of the exposition really varies from one book to the other. I personally found the Lie Algebras book much more readable than the Algebra one. I haven't read any other volume of the Bourbaki's series, so I don't have an opinion on the other chapters. In any case, I'd like to know if one has any idea (or convictions) on the identity of the authors of each volume. Let me start filling the boxes where I am almost convinced I am correct:
$\bullet$ Algebra (at least chapter 4 to 7?) : Adrien Douady (may be wrong as he is said to have joined after the beginning of the writting of Algebra 4-7)?
$\bullet$ Espaces vectoriels topologiques (the whole book?) : Alexandre Grothendieck.
Possible guess following suggestions in the comments:
$\bullet$ Lie Algebras : François Bruhat (in connection with his co-author Jacques Tits)?
$\bullet$ Functions of a real variable : Jean Delsartes?
Any guess for the other chapters/books?
EDIT : Following @abx remark (who actually was one of the later Bourbaki's member, so he can be trusted on that point), one should rather ask for the author of the preliminary draft of each chapter. This, in any case, is what I was looking for. I am definitely not interested in the various identities of the members who polished the initial version of the draft.
EDIT BIS : Matthieu Latapy suggests a very interesting approach using comparison of n-gram distributions between the Bourbaki's chapters and some contemporary papers of the suspected authors. I must confess I don't have any idea on how to implement that effectively. But I'd very interested to know if it can be used to match François Bruhat with some chapters in Lie-Algebras, Adrien Douady with some chapters in Algebra and Commutative Algebra with Samuel/Chevalley/Cartier.
Best Answer
I think the whole idea is wrong. As you can see from the Bourbaki archives, Bourbaki worked as follows: one member would write a rough first draft, this would be read in the next meeting, criticized, heavily modified, then another member would write a new version, and so on. It is impossible to attribute any of the books to one author. By the way, all guesses in the post or in the comments are wrong: Algebra 4-7 was started much before Douady joined Bourbaki, Tits was never a member, etc.