This textbook for beginning graduate students is a general introduction to the dynamics of astrophysical fluids for students with a knowledge of basic physics at undergraduate level. No previous knowledge of fluid dynamics or astrophysics is required because the author develops all new concepts in context. The first four chapters cover classical fluids, relativistic fluids, photon fluids and plasma fluids, with many cosmic examples being included. The remaining six chapters deal with astrophysical applications: stars, stellar systems, astrophysical plasmas, cosmological applications and large scale structure of the Universe. Astrophysical fluid dynamics is a promising branch of astronomy, with wide applicability. This textbook considers the role of plasma and magnetism in planets, stars, galaxies, the interplanetary, interstellar and intergalactic media, as well as the Universe at large.