This book offers a brief introduction to the Physics of Fluids. It considers first the case of ideal fluids where viscous friction and thermal conduction processes are neglected. Once Euler’s equation is derived in Chapter 2, the Navier-Stokes hydrodynamic equations are obtained and applied to some simple physical situations in Chapter 3. Chapter 4 addresses the problem of thermal conduction in simple fluids while Chapter 5 extends the equations of fluid dynamics to the case of multicomponent fluid systems. The stability of the hydrodynamic equations is analyzed in Chapter 6 where explicit forms for the hydrodynamic modes are obtained. The book ends in Chapter 7 with a microscopic derivation of the hydrodynamic equations for a dilute gas from the famous Boltzmann kinetic equation. The book covers the content of a semester and can be employed as a textbook to follow the course "Physics of Fluids" of the Physics grade.