This fundamental course develops the conservation laws governing the motion of a continuum and applies the results to the case of Newtonian fluids, which leads to the Navier-Stokes equations. From these general equations, some theorems are derived from specific circumstances such as incompressible fluids or inviscid fluids. Basic solutions to, and properties of, the governing equations are explored for the case of viscous, but incompressible, fluids. Topics included involve exact solutions, low-Reynolds-number flows, laminar boundary layers, flow kinematics, and 2D potential flows.