These are lecture notes for a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September 1-10, 1997.
1. Commutative geometry from the noncommutative point of view.
2. Spectral triples on the Riemann sphere.
3. Real spectral triples, the axiomatic foundation.
4. Geometries on the noncommutative torus.
5. The noncommutative integral.
6. Quantization and the tangent groupoid.
7. Equivalence of geometries.
8. Action functionals. |