This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest. "The author presents rigorous mathematical theory and offers deep insights ... contribution of these notes to the modern literature is very valuable and unique ... essentially self-contained and does not require prior knowledge of fluid dynamics ... should be of interest to anyone in the community of atmosphere/ocean science, from graduate students to advanced researchers." ---- Mathematical Reviews