In this talk, we will briefly revise the algebraic formulation of classical and quantum physical systems in terms of $C^\ast$-algebras. We will check that, in the case of atomic systems, this description is actually better motivated than the usual Dirac-von Neumann axiomatic structure of Quantum Theory, which becomes nearly inevitable in this context — except for the so-called measurement problem and the reduction of the wave packet, concerning the interaction between the quantum system and the measuring apparatus, which will be briefly analyzed.