Preface; Acknowledgements; Amalie Emmy Noether: a life for mathematics; Notation; Acronyms; Part I. Preliminaries: 1. The concept of symmetry; 2. The two Noether theorems; 3. Applications of the Noether first theorem to fields and particles; 4. Theories of gravity: an overview; Part II. The Noether Symmetry Approach: 5. From the Noether theorem to the Noether symmetry approach; 6. The extensions of GR, TEGR and STEGR; 7. Higher-order extensions with the Gauss–Bonnet invariant; 8. Extensions with higher derivatives or R and T; 9. Scalar-tensor theories of gravity; 10. Non-local gravity; 11. Noether symmetries in Bianchi universes; 12. The Noether approach in spherical symmetry; Part III. Applications: 13. Applications to solar system, stars and our galaxy; 14. Applications to galaxies; 15. Applications to cosmology; 16. Applications to quantum cosmology; 17. Strings, swampland, renormalizability and viability; Epilogue; Appendices; References; Index.