IntГ©gration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especiallyВ General Topology andВ Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author'sВ ThГ©ories Spectrales [MRВ 35 #4725], an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.
The first volume of the English translation comprises Chapters 1-6; the presentВ volume completes the translation with the remaining Chapters 7-9.
Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chs. 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations).