This classic text offers a thorough, clear and methodical introductory exposition of the mathematical theory of fluid motion, useful in applications to both hydrodynamics and aerodynamics. Departing radically from traditional approaches, the author bases the treatment on vector methods and notation with their natural consequence in two dimensions - the complex variable.New features in this edition include: a chapter bringing together various exact treatments of two-dimensional motion with a free surface in a gravitational field, followed by one dealing with approximations (mostly linearized) relevant to this but with emphasis on waves; a chapter on tensor methods applied to the flow of viscous fluids; a chapter on flow with small Reynolds' number, including an account of a novel application of the complex variable to Stokes' flow; and an outline of the theory of two-dimensional laminar flow in a boundary layer.Prerequisites are restricted to a knowledge of elementary calculus since any additional mathematics is introduced as required, making this a self-contained treatment. Nearly 400 diagrams help illustrate the text and over 600 exercises are collected into sets of examples at the end of each chapter.