The Radon transform, which represents the scattering data arising from a tomographic scan, underpins the mathematical foundations of medical imaging. This book surveys the mathematics behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled physics or hybrid techniques, including thermoacoustic tomography. Presented in this treatment are explanations of important concepts such as inversion, stability, incomplete data effects, the role of interior information, and other critical issues. In addition to emphasising mathematical ideas from across the spectrum of medical imaging modalities, the author provides a vast bibliography, and appendices covering notation, Fourier analysis, geometric rays, and linear operators. Graduate students and researchers in mathematics, physics, and engineering who are interested in medical imaging will find this book to be an invaluable resource.