Geometrodynamics of non-relativistic continuous media, I.

In order to formulate the non-relativistic continuum mechanics as a unified field theory on Galilei space-time $ M$, the geometrical structure of $ M$ is considered and the space time resolution of bundles of geometric objects on $ M$ are analysed in detail. In particular, the conceptof geometric object gives rigorous meaning to the concept of observed physical quantity. It clarifies the ambiguity of why ''frame dependent'' quantities are useful, even essential, in the kinematic of description of continuum mechanical bodies. Moreover, it clarifies the paradosical nature of ''frame indifferent statements about frame dpendent quantities''. These turn out to be simply statements about fields of geometric objects which are not tensor fields.