Includes bibliographical references (pages 255-269) and index.
Chapter 1: Gravity and Matter in Noncommutative Geometry -- Chapter 2: Renormalization Group Flows and Early Universe Models -- Chapter 3: Cosmic Topology -- Chapter 4: Algebro-geometric models in Cosmology -- Chapter 5: Mixmaster Cosmologies -- Chapter 6: The Spectral Action on Bianchi IX Cosmologies -- Chapter 7: Motives and Periods in Cosmology -- Chapter 8: Fractal and Multifractal Structures in Cosmology -- Chapter 9: Noncommutative Quantum Cosmology.