Geodesic
Introduction to noncommutative differential geometry
Lobachevskii journal of mathematics, Tome 4 (1999), pp. 13-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is getting a major understanding that the function ring of the underlying space of the quantum world is not a commutative ring, and the underlying space itself is not even a point set. In spite of this, the underlying space of the quantum world should be a continuum, on which one can make a calculus. We hope we can see such mathematics in the coming century. This article is a survey of such effort or trial to make such calculus. However, this article does not give a bird-eye-view of the noncommutative world but this gives several toys which come from the noncommutative world. 
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     author = {H. Omori},
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H. Omori. Introduction to noncommutative differential geometry. Lobachevskii journal of mathematics, Tome 4 (1999), pp. 13-46. http://geodesic.mathdoc.fr/item/LJM_1999_4_a1/