Treats the origin of magnetic fields in planets, stars and galaxies, and the manner of their evolution over time.

Keith Moffatt FRS is Emeritus Professor of Mathematical Physics at the University of Cambridge. He has served as Head of the Department of Applied Mathematics and Theoretical Physics, and as Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge. A former editor of the Journal of Fluid Mechanics, he has published papers in fluid dynamics and magnetohydrodynamics, and was a pioneer in the development of topological fluid dynamics. He is a Fellow of the Royal Society, a member of Academia Europæa, and a Foreign Member of the Academies of France, Italy, the Netherlands and USA. He has been awarded numerous prizes, most recently the 2018 Fluid Dynamics Prize of the American Physical Society.

Preface; Part I. Basic Theory and Observations: 1. Introduction; 2. Magnetokinematic preliminaries; 3. Advection, distortion and diffusion; 4. The magnetic field of the Earth and planets; 5. Astrophysical magnetic fields; Part II. Foundations of Dynamo Theory: 6. Laminar dynamo theory; 7. Mean-field electrodynamics; 8. Nearly axisymmetric dynamos; 9. Solution of the mean-field equations; 10. The fast dynamo; Part III. Dynamic Aspects of Dynamo Action: 11. Low-dimensional models of the geodynamo; 12. Dynamic equilibration; 13. The geodynamo: instabilities and bifurcations; 14. Astrophysical dynamic models; 15. Helical turbulence; 16. Magnetic relaxation under topological constraints; 17. Magnetic relaxation in a low-ß plasma; Appendix. Orthogonal curvilinear coordinates; References; Author index; Subject index.