Continuum hypothesis. Basics of vector calculus. Eulerian and Lagrangian description of the flow. Decomposition of motion. Conservation of mass, momentum, and energy. Constitutive equations for Newtonian fluids. Navier Stokes equations. Dimensional analysis and Pi theorem. Exact solution for unidirectional flows. Other exact solutions of laminar flows. Stokes flows and lubrication theory. Vorticity dynamics. Kelvin’s circulation theorem. Geostrophic flows. Velocity potential and potential flows. D’Alembert’s paradox and Blasius drags laws. Conformal mapping.