Georgia Institute of Technology College of Sciences

This series of lecture will try to give some basic facts about Noncommutative Geometry for the members of the School of Mathematics who want to learn about it. In the first lecture, the basics tools will be presented, (i) the philosophy and the notion of space, and (ii) the notion of C*-algebra, (iii) groupoids. As many examples as possible will be described to illustrate the purpose. In the following lectures, in addition to describing these tools more thoroughly, two aspects can be developed depending upon the wishes of the audience: A- Topology, K-theory, cyclic cohomology B- Noncommutative metric spaces and Riemannian Geometry.