The most difficult reconstruction of a reduction is provided by quantum mechanics (QM) in its relation to classical mechanics (CM) and classical statistical mechanics (CSM). We begin this task with a preparatory section in which we fix our reduction partners and introduce the special problem posed here. As a further preliminary, we explain the widely known Ehrenfest theorems in their partial reductionist function. In the main, we try to reconstruct two state and observable transformations as a more comprehensive reduction from CSM to QM, which also captures the dynamics of the two theories—the Liouville equation of CSM and the Schrödinger equation of QM. For the observables, these transformations are a standard transformation and the Weyl transformation. For the states, they are the transformation used by Bohm in his first theory of hidden parameters (already known from the WKB method) and the transformation first given by Wigner for computational reasons. Transformations of observables and states transform only one representation of QM into another. They induce transformations for further structures built from states and observables, such as the mean value function, the pure states, the functional dependence of observables, and so on. The Schrödinger equation, for example, by applying Bohm’s transformation, takes a form which permits to compare it directly with the classical Hamilton-Jacobi equation; by applying Wigner’s transformation, quite the same happens with respect to the classical Liouville equation. But, for this case, reliable results are missing, as already before for the case of functional dependence.