Fluid dynamical forces drive most of the fundamental processes in the Universe and so play a crucial role in our understanding of astrophysics. This comprehensive textbook introduces the necessary fluid dynamics to understand a wide range of astronomical phenomena, from stellar structures to supernovae blast waves, to accretion discs. The authors approach is to introduce and derive the fundamental equations, supplemented by text that conveys a more intuitive understanding of the subject, and to emphasise the observable phenomena that rely on fluid dynamical processes. The textbook has been developed for use by final year undergraduate and starting graduate students of astrophysics, and contains over fifty exercises. It is based on the authors' many years of teaching their astrophysical fluid dynamics course at the University of Cambridge.