The course will address elementary concepts in continuum mechanics: conserved scalar and vector fields, and the stress tensor, and Lagrangian and Eulerian descriptions of the balance laws. Examples of motion - extensional, shear, and rigid body motion will be discussed, along with the basic equations of elasticity. We will study the basic equations of fluid mechanics, the Navier-Stokes equations, and its solutions in special cases, for viscous flows and low Reynolds number hydrodynamics.