  A new picture of Quantum Mechanics based on the theory of groupoids is
presented. This picture provides the mathematical background for Schwinger's
algebra of selective measurements and helps to understand its scope and
eventual applications. In this first paper, the kinematical background is
described using elementary notions from category theory, in particular the
notion of 2-groupoids as well as their representations. Some basic results are
presented, and the relation with the standard Dirac-Schr\"odinger and
Born-Jordan-Heisenberg pictures are succinctly discussed.
