Martensites are crystalline solids that display dazzling patterns at the microscopic scales. This microstructure gives rise to unusual macroscopic properties like the shape-memory effect. Starting with the crystalline structure, this book describes a theoretical framework for studying martensites and uses the theory to explain why these materials form microstructure. The macrostructure consequences of the microstructure are subsequently discussed. Complete with a piece of shape-memory wire and numerous examples from real materials, this book represents a successful case study in multiscale modeling, giving a clear understanding of the link between microstructure and macrostructure properties. Beautifully written, in a most clear and pedagogical manner, it holds appeal for a broad audience. On the one hand, it introduces modern modeling techniques to those trained in materials science, mechanics and physics and shows how these techniques can be used in real-world problems. On the other hand, it introduces physical phenomena to those trained in mathematics, and demonstrates how such phenomena give rise to interesting mathematical problems.