The main magnetic field of the Earth is a complex phenomenon. To understand its origins in the fluid of the Earth's core, and how it changes in time requires a variety of mathematical and physical tools. This book presents the foundations of geomagnetism, in detail and developed from first principles. The book is based on George Backus' courses for graduate students at the University of California, San Diego. The material is mathematically rigorous, but is logically developed and has consistent notation, making it accessible to a broad range of readers. The book starts with an overview of the phenomena of interest in geomagnetism, and then goes on to deal with the phenomena in detail, building the necessary techniques in a thorough and consistent manner. Students and researchers will find this book to be an invaluable resource in the appreciation of the mathematical and physical foundations of geomagnetism.