Geodesic
Introduction to noncommutative differential geometry
Lobachevskii journal of mathematics, Tome 4 (1999), pp. 13-46 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     title = {Introduction to noncommutative differential geometry},
     journal = {Lobachevskii journal of mathematics},
     pages = {13--46},
     year = {1999},
     volume = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_1999_4_a1/}
}
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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/