This is the first textbook to cover the essential aspects of the topic at a level accessible to students. While focusing on applications in solid earth geophysics, the book also includes excursions into helioseismology, thereby highlighting the strong affinity between the two fields. The book provides a comprehensive introduction to seismic tomography, including the basic theory of wave propagation, the ray and Born approximations required for interpretation of amplitudes, and travel times and phases. It considers observational features while also providing practical recommendations for implementing numerical models. Written by one of the leaders in the field, and containing numerous student exercises, this textbook is appropriate for advanced undergraduate and graduate courses. It is also an invaluable guide for seismology research practitioners in geophysics and astronomy. Solutions to the exercises and accompanying tomographic software and documentation can be accessed online from www.cambridge.org/9780521882446.