This self-contained work teaches second and third-year undergraduates in mathematics and mathematical physics the principles of the basic processes governing the motion of incompressible fluids. It will also serve as a reference book for mathematically-minded physicists and engineers from undergraduate level upwards who need a treasury of the main facts, equations and results in incompressible flow. The authors have selected the important facts and organized them into a clear and logical account of the subject. They have achieved this by combining mathematical precision with physical relevance. The first half of the book discusses the classical theories of hydrodynamics and forms a sound basis for the subsequent study of more modern developments. This part presupposes a knowledge of a complex variable theory and vector analysis. A grounding in cartesian tensors is a prerequisite for the latter half of the book which considers how the classical theories apply to the dynamics of real fluids, boundary layers and turbulence. This unusual breadth of coverage, and mathematical precision, have been achieved by omitting inessential calculations and avoiding many lengthy solutions to problems. Methods of solution are merely outlined (with hints where necessary) so that the reader is encouraged to think, deduce and interpret, rather than to memorize forms. Comprehension of the material is reinforced by examination-type questions at the end of each chapter.