  In the two papers of this series, we initiate the development of a new
approach to implementing the concept of symmetry in classical field theory,
based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are
the appropriate mathematical tools to describe local symmetries when gauge
transformations are combined with space-time transformations. Here, we outline
the basis of the program and, as a first step, show how to (re)formulate
Noether's theorem about the connection between symmetries and conservation laws
in this approach.
