"Smooth Manifolds and Observables" by Jet Nestruev.

The actual team of Authors: A. M. Astashev, A. V. Bocharov, S. V. Duzhin, A. B. Sossinsky, A. M. Vinogradov, M. M. Vinogradov

Springer-Verlag, Graduate Texts in Mathematics, vol. 220, 2002

A Russian answer to Bourbaki (see the preface to the book).