  In this paper we present a unified algebraic framework to discuss the
reduction of classical and quantum systems. The underlying algebraic structure
is a Lie-Jordan algebra supplemented, in the quantum case, with a Banach
structure. We discuss the reduction by symmetries, by constraints as well as
the possible, non trivial, combinations of both. We finally introduce a new,
general framework to perform the reduction of physical systems in an algebraic
setup.
