There are two main fluids found on our Planet Earth, namely water and air. Their appearances on Earth’s surface make our planet habitable for living organisms. This chapter focuses on the fundamental fluid dynamics used in modeling geophysical flows. All fluid motions on the Earth’s surface can, in principle, be formulated with respect to a fixed frame of reference, such as a distant star. In fluid mechanics, Eulerian formulation employs the idea of a control volume. For any fluid, the density is a function of temperature and pressure and this is known as the equation of state. In nonrotating fluid flows, the ratio of inertial and viscous forces is called the Reynolds number and it can be expressed in terms of the Rossby number and the Ekman number. Vorticity cannot be generated inside the fluid, and therefore, it must be generated from the boundary. Vorticity implies the local rotation of a fluid element.