In this chapter we will introduce the rules to translate classical observables in phase-space representation to hermitian operators in the formal space of wavefunctions (Hilbert space). It is furthermore proven that the classical equations of motion also hold for the expectation values of the corresponding quantum operator (Ehrenfest theorem). The formal translation of the Poisson brackets in classical mechanics to commutators in quantum physics is derived and it is shown, that the commutators follow the same algebra as the Poisson brackets.