This remarkable collaboration between a mathematical physicist and a philosopher of science is concerned with foundational and conceptual issues in seismology. Their aim is to present mathematical, physical, and philosophical topics in a clear way and to clarify them when this is possible. They provide an extensive philosophical discussion of the methods of science and show how seismology fits in. They explain with care and precision the basic structure of seismology, which is built on classical continuum mechanics. Not only do they explain how various models work in seismology, but they include an extensive discussion of the nature of models and idealizations.