A readable and user-friendly introduction to fluid mechanics, this high-level text is geared toward advanced undergraduates and graduate students. Mathematicians, physicists, and engineers will also benefit from this lucid treatment. The book begins with a derivation of the equations of fluid motion from statistical mechanics, followed by examinations of the classical theory and a portion of the modern mathematical theory of viscous, incompressible fluids. A considerable part of the final chapters is devoted to the Navier-Stokes equations. The text assumes a familiarity with functional analysis and some complex variables, and it includes an especially valuable discussion of the modern function theoretic approach to solving partial differential equations. Numerous exercises appear throughout the text.