An exact answer to a mathematical problem is usually the best answer but sometimes an exact answer is either unobtainable or unhelpful (or both). In that case, an approximation is the likely best choice. This book shows how to create and work with rigorous approximations using the notation and logic of asymptotics. Asymptotic approximations are important throughout mathematics and computer science. This book can be used as a supplementary text for a college course or for individual self-study.In addition to a solid introduction to asymptotic notation, methods, and formulas, we provide an extensive suite of exercises (with complete solutions) to ensure mastery.