The continuum assumption and the Knudsen number. Strain and stress in ideal, Newtonian and rheological fluids. Eulerain and Lagrangian temporal derivatives in the continuity equation. Body and surface hydrodynamic forces composing the Navier-Stokes equation. Energy balance and the Bernoulli potential. Vorticity and circulation in barotropic and baroclinic flows. Potential flow and the Cauchy-Riemann conditions. Flow around bodies with and without circulation. The Magnus effect and the Kutta-Zhukowsky lift theorem. Waves in continuous media: sound waves and shallow and deep gravity waves. Phase versus group velocity and dispersion relation. Lagrangian trajectories and the Stokes drift. Instability of shear flow: The Rayleigh and Fjortoft necessary conditions for shear instability and the conservation of wave-action and pseudo-energy. Kelvin-Helmholtz instability and the Richardson number criterion. Thermal instability: Rayleigh-Taylor and Rayleigh-Benard convection. Spectral truncation and the Lorenz low order chaos model. The butterfly effect and the notion of strange attractor.