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This text offers a comprehensive, self-contained, and unified treatment of the theory and application of mathematical methods behind modern-day financial mathematics. It introduces the financial theory and the relevant mathematical methods in a mathematically rigorous yet student-friendly and engaging style. The text provides complete and in-depth coverage of both discrete- and continuous-time financial models and pricing theory. It also includes numerous examples, exercises, fully worked out solutions, and multiple problem-solving approaches. A solutions manual is available upon qualifying course adoption.