The study of fluid dynamics is a central theme in modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics that is suitable for all undergraduates coming to the subject for the first time. Students need only a basic knowledge of vector calculus, complex analysis, and simple methods of solving differential equations. Numerous exercises (with hints and answers) illustrate the main ideas and serve to organize the reader's understanding. The wide range of topics discussed include inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flows, along with historical information and many references to important experiments. This is a comprehensive and absorbing introduction to the mathematical study of fluid behavior.