A geometrically oriented introduction to the calculus of vector and tensor fields on three-dimensional Euclidean point space, with applications to the kinematics of point masses, rigid bodies, and deformable bodies. Aside from conventional approaches based on working with Cartesian and curvilinear components, coordinate-free treatments of differentiation and integration will be presented. Connections with the classical differential geometry of curves and surfaces in three-dimensional Euclidean point space will also be established and discussed.