Elements of Mathematics Functions of a Real Variable: Elementary Theory

This is an English translation of Bourbaki’s Fonctions d'une Variable Réelle. Coverage includes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.

From the reviews:

"Nicolas Bourbaki is the name given to a collaboration of mainly French mathematicians who wrote a series of textbooks that started from basics and aimed to present a complete picture of all essential mathematics. ... The Elements of Mathematics series is the result of this project. ... The translation is true to the original. ... should be part of any good library of mathematics books." (Partrick Quill, The Mathematical Gazette, March, 2005)

"The book under review is the latest installment in the translation into English of the voluminous Bourbaki exercise. ... Respectable mathematics libraries should have this book on their shelves. ... the book may be judged as an unqualified intellectual success and the publisher and the translator are to be congratulated on making it available in English." (Barry D.Hughes, The Australian Mathematical Society Gazette, Vol. 43 (1), 2005)