Abstract: The “geometrization" of mechanics (whether classical, relativistic or quantum) is almost as old as modern differential geometry, and it nowadays textbook material. The formulation of a mathematically-sound theory for the mechanics of continuum media is still a subject of ongoing research. In this lecture I will present a geometric formulation of continuum mechanics, starting with the definition of the fundamental physical observables, e.g., force, deformation, stress and traction. The outcome of this formulation is a generalization of Newton’s "F=ma” equation for continuous media.