How can the drag coefficient of a car be reduced? What factors govern the variation in the shape of the Earth's magnetosphere? What is the basis of weather prediction? These are examples of problems that can only be tackled with a sound knowledge of the principles and methods of fluid dynamics. This important discipline has applications which range from the study of the large-scale properties of the galaxies to the design of high precision engineering components. This book introduces the subject of fluid dynamics from the first principles. The first eleven chapters cover all the basic ideas of fluid mechanics, explaining carefully the modelling and mathematics needed. The last six chapters illustrate applications of this material to linearised sound and water waves, to high speed flow of air, to non-linear water waves on channels, and to aerofoil theory. Over 350 diagrams have been used to illustrate key points. Exercises are included to help develop and reinforce the reader's understanding of the material presented. References at the ends of each chapter serve not only to guide readers to more detailed texts, but also list where alternative descriptions of the salient points in the chapter may be found. This book is an undergraduate text for second or third year students of mathematics or mathematical physics, who are taking a first course in fluid dynamics.