A valuable synthesis of the physics of magmatism for students and scholars Magma genesis and segregation have shaped Earth since its formation more than 4.5 billion years ago. Now, for the first time, the mathematical theory describing the physics of magmatism is presented in a single volume. The Dynamics of Partially Molten Rock offers a detailed overview that emphasizes the fundamental physical insights gained through an analysis of simplified problems. This textbook brings together such topics as fluid dynamics, rock mechanics, thermodynamics and petrology, geochemical transport, plate tectonics, and numerical modeling. End-of-chapter exercises and solutions as well as online Python notebooks provide material for courses at the advanced undergraduate or graduate level. This book focuses on the partial melting of Earth’s asthenosphere, but the theory presented is also more broadly relevant to natural systems where partial melting occurs, including ice sheets and the deep crust, mantle, and core of Earth and other planetary bodies, as well as to rock-deformation experiments conducted in the laboratory. For students and researchers aiming to understand and advance the cutting edge, the work serves as an entrée into the field and a convenient means to access the research literature. Notes in each chapter reference both classic papers that shaped the field and newer ones that point the way forward. The Dynamics of Partially Molten Rock requires a working knowledge of fluid mechanics and calculus, and for some chapters, readers will benefit from prior exposure to thermodynamics and igneous petrology. The first book to bring together in a unified way the theory for partially molten rocks - End-of-chapter exercises with solutions and an online supplement of Jupyter notebooks - Coverage of the mechanics, thermodynamics, and chemistry of magmatism, and their coupling in the context of plate tectonics and mantle convection - Notes at the end of each chapter highlight key papers for further reading “It is no exaggeration to say that magmatism is the reason why the Earth is as it is today. Proceeding systematically from simple to complex models, Richard Katz comprehensively surveys the physics and chemistry of partial melting with elegance, pedagogical clarity, and deep physical insight. This book will be the definitive treatment of its subject for many years to come.” ―Neil Ribe, University of Paris-Saclay “The twin processes of partial melting and melt migration are essential features of the evolution of all terrestrial planets. Yet, the theory of partially molten rock, developed through a series of dense papers in the primary literature, has hitherto only been available to experts. In this appealing and accessible book, Katz brings all the necessary information together to introduce the field to newcomers and guides them to the most cutting-edge developments.” ―Paul D. Asimow, California Institute of Technology “Igneous petrology, the study of melts produced from the Earth's interior, has a long history. Yet until about forty years ago, petrologists had almost no interest in how such melts formed. Since then a new branch of fluid dynamics has developed that explores how melts separate from solid residue. Deriving the governing equations and their solutions, this excellent book provides the basic fluid dynamical understanding that will underpin all future work in this important field.” ―Dan McKenzie, emeritus professor of earth sciences, University of Cambridge "Filling an important gap in textbooks that describe Earth dynamics, this book provides an overview of the mathematical description of magma dynamics that is broad, encompassing, and detailed. Katz describes with clarity fairly complex mathematical physics and the text is well written. A pleasure to read." ―Peter van Keken, Carnegie Institution for Science "Covering the two-phase formalism that has been widely used in geophysics to discuss magma extraction, this book makes a significant contribution to the field. No other books exist on this subject." ―Yanick Ricard, CNRS/ENS-Lyon Richard F. Katz is professor of geodynamics at the University of Oxford.