Quantum systems with finite Hilbert space are considered. Position and mo- \nmentum states and their relation through a Fourier transform, displacement \nin the position-momentum phase-space, and symplectic transformations are \nintroduced and their properties are studied. Symplectic Sp(2l;Zp) trans- \nformations in l-partite finite system are explicit constructed. The general \nmethod is applied to bi-partite and tri-partite systems. The effect of these \ntransformations on the correlations is discussed. Entanglement calculations \nbetween the subsystems in a bi-partite system and a tri-partite system are \npresented. The effect of measurements is also studied.