Magnetohydrodynamics (MHD) plays a crucial role in astrophysics, planetary magnetism, engineering and controlled nuclear fusion. This comprehensive textbook emphasizes physical ideas, rather than mathematical detail, making it accessible to a broad audience. Starting from elementary chapters on fluid mechanics and electromagnetism, it takes the reader all the way through to the latest ideas in more advanced topics, including planetary dynamos, stellar magnetism, fusion plasmas and engineering applications. With the new edition, readers will benefit from additional material on MHD instabilities, planetary dynamos and applications in astrophysics, as well as a whole new chapter on fusion plasma MHD. The development of the material from first principles and its pedagogical style makes this an ideal companion for both undergraduate students and postgraduate students in physics, applied mathematics and engineering. Elementary knowledge of vector calculus is the only prerequisite. Review of previous edition: "… an excellent book, which provides a refreshing introduction and a welcome addition to the MHD literature." A. M. Soward, Journal of Fluid Mechanics Review of previous edition: "The language of this book is simple, vivid, yet fully scientific. It is a real pleasure to read … worth recommending, not only to students, but also to everyone who is interested in MHD, particularly to theoreticians who, as a rule, know almost nothing about metallurgical applications of MHD." Applied Mechanics Review Review of previous edition: "Like other texts in the series, the typography is easy on the eyes and the price easy on the purse. All in all, a wonderful introduction to the subject and more!" Stanley A. Berger, Physics Today Review of previous edition: "… a thorough introduction to conducting fluid mechanics … an excellent and informative book that can be well recommended." S. W. H. Cowley, Contemporary Physics Review of previous edition: "The author writes lucidly and maintains the reader's interest in several ways: he formulates arguments provocatively, sometimes as paradoxes; he provides apt quotations; he points to exciting applications; and he enlivens his text with historical snippets … It is written with love, and in a completely consistent style." Paul H. Roberts, SIAM Review Review of previous edition: "The book is unique in bringing together a number of diverse topics … [It] makes for rewarding reading, and I recommend it to all students of MHD, no matter what their persuasion. It would be an excellent textbook for students with interest in the engineering applications, but also will serve as a perfect complementary text for an introductory plasma MHD course." Elena V. Belova, American Journal of Physics 'The rich scholarship presented in this monograph is a result of the author’s ongoing study of these concepts … This careful documentation, also provided for modern technology, gives the reader an exceptional glimpse into this field.' J. W. Jerome, MathSciNet 'This book is at once a useful basic textbook introducing the elements of electromagnetism and fluid dynamics and, at the same time, an informative research monograph targeting professional researchers in industry and academia.' K. Alan Shore, Optics & Photonics News Comprehensive textbook prioritising physical ideas over mathematical detail. New material includes fusion plasma magnetohydrodynamics. P. A. Davidson is a professor in the Department of Engineering at the University of Cambridge. He has authored over 100 publications in the fields of magnetohydrodynamics and turbulence, including the books Turbulence: An Introduction for Scientists and Engineers (2015) and Turbulence in Rotating, Stratified and Electrically Conducting Fluids (2013). He is also an associate editor of the Journal of Fluid Mechanics.