  The fundamental ideas and tools of the global geometric formulation of stress
and hyper-stress theory of continuum mechanics are introduced. The proposed
framework is the infinite dimensional counterpart of statics of systems having
finite number of degrees of freedom, as viewed in the geometric approach to
analytical mechanics. For continuum mechanics, the configuration space is the
manifold of embeddings of a body manifold into the space manifold. Generalized
velocity fields are viewed as elements of the tangent bundle of the
configuration space and forces are continuous linear functionals defined on
tangent vectors, elements of the cotangent bundle. It is shown, in particular,
that a natural choice of topology on the configuration space, implies that
force functionals may be represented by objects that generalize the stresses of
traditional continuum mechanics.
