The Navier–Stokes equations are a set of partial differential equations that describe the behavior of Newtonian fluids (e.g., water and air). The equations were formulated by French engineer Claude-Louis Navier and British-Irish physicist George Gabriel Stokes over a period spanning almost three decades. When used in conjunction with the Bernoulli equation (named for Swiss physicist and mathematician Daniel Bernoulli), they represent the pillars of fluid mechanics and are some of the most well-known equations within science and engineering. In this chapter, we will introduce these equations from both a conceptual and mathematical perspective.