Recently, I found an old collection of books, authored by Nicolas Bourbaki. Turned out that he was an interesting person :-). I looked more closely and found out that his books are cited by many modern mathematical books on various topics. In the same time, these books are not recommended anywhere anymore. The promise that they present self-contained treatment of mathematics seems very appealing to me. Are there any caveats? Are they old in content or notation?
at the time they were originally published, they were revolutionary. they represent a certain "approach" to mathematics, which might be summed up as "an austere axiomatic method". certain things have happened since the publication of the "fascicules" that have made Bourbaki somewhat obsolete:
1. The development of category theory as a basis for algebra: especially commutative algebra and homology.
2. The development of algorithmic solutions/approaches due in part to the ubiquity of high-speed computers.
3. The alternative development of functional analysis driven by research into theoretical physics.
4. the incorporation of "the Bourbaki method" into much of what is now standard mathematical curriculum.
Bourbaki is dense, and each successive volume assumes the previous ones. That said, it is certainly "worth reading", the authors (for Bourbaki is a pseudonym for a collective of French mathematicians, most notably Henri Cartan, Andre Weil, Jean Dieudonne, Alexander Grothendieck, Jean-Paul Serre, and Serge Lang, that spring immediately to mind), were first-rate mathematicians. Bourbaki was "state-of-the-art" in the 1960s, now, not so much. But as you can see, by the many citations, they were very influential.
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