# Introduction to noncommutative differential geometry

## (*Lobachevskii Journal of Mathematics, Volume IV*)

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.