  We present a unified approach to representations of quantum mechanics on
noncommutative spaces with general constant commutators of phase-space
variables. We find two phases and duality relations among them in arbitrary
dimensions. Conditions for physical equivalence of different representations of
a given system are analysed. Symmetries and classification of phase spaces are
discussed. Specially, the dynamical symmetry of a physical system is
investigated. Finally, we apply our analyses to the two-dimesional harmonic
oscillator and the Landau problem.
