Noncommutative Geometry for Pedestrians

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A short historical review is made of some recent literature in the field of noncommutative geometry, especially the efforts to add a gravitational field to noncommutative models of space-time and to use it as an ultraviolet regulator. An extensive bibliography has been added containing reference to recent review articles as well as to part of the original literature.
Lecture given at the International School of Gravitation, Erice, 28 pages, Latex

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