  We analysis the quantum Hall effect exhibited by a system of particles moving
in a higher dimensional space. This can be done by considering particles on the
Bergman ball {\bb{B}_{\rho}^d} of radius \rho in the presence of an external
magnetic field B and investigate its basic features. Solving the corresponding
Hamiltonian to get the energy levels as well as the eigenfunctions. This can be
used to study quantum Hall effect of confined particles in the lowest Landau
level where density of particles and two point functions are calculated. We
take advantage of the symmetry group of the Hamiltonian on {\bb{B}_{\rho}^d} to
make link to the Landau problem analysis on the complex projective spaces CP^d.
In the limit \rho\lga\infty, our analysis coincides with that corresponding to
particles on the flat geometry {\bb{C}^d}. This task has been done for d=1, 2
and finally for the generic case, i.e. d \geq 3.
