Containing many results that are new or exist only in recent research articles, this text portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. Taking a top-down approach, the author shows readers how to build and use models. The text includes exercises and real-world examples, along with code, tables, and figures accessible on the authors website. A solutions manual is available for qualifying instructors.