David Sandwell developed this advanced textbook over a period of nearly 30 years for his graduate course at Scripps Institution of Oceanography. The book augments the classic textbook Geodynamics by Don Turcotte and Jerry Schubert, presenting more complex and foundational mathematical methods and approaches to geodynamics. The main new tool developed in the book is the multi-dimensional Fourier transform for solving linear partial differential equations. The book comprises nineteen chapters, including: the latest global data sets; quantitative plate tectonics; plate driving forces associated with lithospheric heat transfer and subduction; the physics of the earthquake cycle; postglacial rebound; and six chapters on gravity field development and interpretation. Each chapter has a set of student exercises that make use of the higher-level mathematical and numerical methods developed in the book. Solutions to the exercises are available online for course instructors, on request.