Can the Bourbaki series be used profitably by undergraduates and high school students?Are we the target audience? I came across the N.Bourbaki texts while surfing the internet(I have not had the opportunity to access them though) and was a bit amazed by the Wikipedia article suggesting they did mathematics very rigorously.
1) No, you are not the target audience.
2) No undergraduate is.
3) For every subject an undergraduate might want to learn there are books better suited than Bourbaki: ask about them here.
4) In a strictly historic sense the target audience was Henri Cartan and the aim of Bourbaki was to give him a text from which he could teach Stokes’ theorem rigorously, so that he would stop badgering André Weil. (Bourbaki had estimated in 1934 that it would take six months to write the book)
5) That aim has never been achieved.
6) The thousands of pages written by Bourbaki started as prerequisites for the proof of Stokes’ theorems. Then they decided to forget about Stokes and write a treatise containing all of basic mathematics. They failed to achieve that goal too. (There is for example an allusion to a forthcoming book on numerical mathematics…)
7) At the graduate level certain books by Bourbaki are still arguably the best available references: some volumes in Algebra, Commutative Algebra and Lie Theory come to mind.
8) Bourbaki is not dead: they have published in 2012 a completely modified new version of Algèbre, Chapitre 8, about 3 times the size of the old version, published in 1958. (Recall that in 1934 they had estimated that the whole treatise would have been written within 6 months…)
Bourbaki is less and less dead: in 2016 they published the fat volume
Topologie Algébrique: Chapitres 1 à 4.
Here is a preview on Google Books (click on Aperçu du livre, just below the first image).