This text introduces readers to magnetohydrodynamics (MHD), the physics of ionised fluids. Traditionally MHD is taught as part of a graduate curriculum in plasma physics. By contrast, this text - one of a very few - teaches MHD exclusively from a fluid dynamics perspective, making it uniquely accessible to senior undergraduate students. Part I of the text uses the MHD Riemann problem as a focus to introduce the fundamentals of MHD: Alfvén's theorem; waves; shocks; rarefaction fans; etc. Part II builds upon this with presentations of broader areas of MHD: fluid instabilities; viscid hydrodynamics; steady-state MHD; and non-ideal MHD. Throughout the text, more than 125 problems and several projects (with solutions available to instructors) reinforce the main ideas. Optionally, large-font lesson plans for a 'flipped-style' class are also available to instructors. This book is suitable for advanced undergraduate and beginning graduate students, requiring no previous knowledge of fluid dynamics or plasma physics.

‘A solid introduction to astrophysical magnetohydrodynamics from one of the pioneers in the field, covering both the physics and the mathematics necessary for mastery of the subject. It is the sort of book I wish was available when I was a student.’

James Stone - Princeton University

‘This is an excellent textbook by a leading expert in the field. It provides first-hand guidance into the framework of MHD and its applications. I emphatically recommend it to the entire MHD community - to scientists, students, and lecturers. The book approaches MHD from a particularly intuitive point of view - from the physics of waves mechanics and dynamics, and it also provides deep insight also into the methods for solving the MHD equations. This area of computational fluid dynamics has rapidly developed, governed by both the availability of sophisticated codes, and the increase in computational power. As a teacher I was always looking for a textbook that presents the essential topics in well-ordered portions, including sets of illuminating problems. As a student I would have greatly benefited myself from such a book. Now it is available.’

Christian Fendt - Max Planck Institute for Astronomy, Germany

‘A First Course in Magnetohydrodynamics is an invaluable reference for students and researchers desiring a deeper understanding of MHD wave phenomena and the underpinnings of modern MHD codes. Clarke’s love of the subject shines through in the pedagogical treatment, which features historical anecdotes, detailed derivations, meticulous supporting figures, and intuition-building discussions. The two-part format is ideal for teaching either 10- or 13-week courses, and the extensive problem sets and projects complete the offering. All in all, the text is a magnificent achievement.’

Michael L. Norman - University of California