In this paper, we review Schwinger’s formulation of Quantum Mechanics and argue that the mathematical structure behind Schwinger’s “Symbolism of Atomic Measurements” is that of a groupoid. In this framework, both the Hilbert space (Schrödinger picture) and the [Formula: see text]-algebra (Heisenberg picture) of the system turn out to be derived concepts, that is, they arise from the underlying groupoid structure.