This book is designed for a first graduate course in fluid dynamics. It focuses on knowledge and methods that find applications in most branches of fluid mechanics, and aims to supply a theoretical understanding that will permit sensible simplifications to be made in the formulation of problems and enable the reader to develop analytical models of practical significance. The study of simplified model problems can be used to guide experimental and numerical investigations. The first part (Chapter 1-4) is concerned entirely with the incompressible flow of homogeneous fluid. Chapters 5 and 6 deal with dispersive waves and acoustics.