This book provides an introduction for graduate students and advanced undergraduate students to the field of astrophysical fluid dynamics. Although sometimes ignored, fluid dynamical processes play a central role in virtually all areas of astrophysics. No previous knowledge of fluid dynamics is assumed. After establishing the basic equations of fluid dynamics and the physics relevant to an astrophysical application, a variety of topics in the field are addressed. There is also a chapter introducing the reader to numerical methods. Appendices list useful physical constants and astronomical quantities, and provide handy reference material on Cartesian tensors, vector calculus in polar coordinates, self-adjoint eigenvalue problems and JWKB theory.