As almost all of the baryonic Universe is fluid, the study of how fluids flow and under which circumstances they achieve equilibrium (i.e., do not flow) is central to modern astrophysics. In order to shed light on this fascinating and ever-evolving research area, we will derive the governing equations of fluid mechanics in their most general form in a mathematically attractive manner and show how these relations can be tailored to tackle with them specific (astrophysical) problems, including convection flows, accretion disks, extragalactic jets, stellar winds, and supernova blast waves.