Chapter 1. Introduction.- Chapter 2. Preliminaries.- Chapter 3. Classical and Noncommutative Geometry.- Chapter 4. Definition and Existence of Quantum Isometry Groups.- Chapter 5. Quantum Isometry Groups of Classical and Quantum.- Chapter 6. Quantum Isometry Groups of Discrete Quantum Spaces.- Chapter 7. Nonexistence of Genuine Smooth CQG Actions on Classical Connected Manifolds.- Chapter 8. Deformation of Spectral Triples and Their Quantum Isometry...