  The quantum-to-classical transition is considered from the point of view of
contractions of associative algebras. Various methods and ideas to deal with
contractions of associative algebras are discussed that account for a large
family of examples. As an instance of them, the commutative algebra of
functions in phase space, corresponding to classical physical observables, is
obtained as a contraction of the Moyal star-product which characterizes the
quantum case. Contractions of associative algebras associated to Lie algebras
are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups are
considered.
