  The multidimensional N=4 supersymmetric quantum mechanics (SUSY QM) is
constructed using the superfield approach. As a result, the component form of
the classical and quantum Lagrangian and Hamiltonian is obtained. In the
considered SUSY QM both classical and quantum N=4 algebras include central
charges, and this opens various possibilities for partial supersymmetry
breaking. It is shown that quantum mechanical models with one quarter, one half
and three quarters of unbroken(broken) supersymmetries can exist in the
framework of the multidimensional N=4 SUSY QM, while the one-dimensional N=4
SUSY QM, constructed earlier, admits only one half or total supersymmetry
breakdown. We illustrate the constructed general formalism, as well as all
possible cases of the partial SUSY breaking taking as an example a direct
multidimensional generalization of the one-dimensional N=4 superconformal
quantum mechanical model. Some open questions and possible applications of the
constructed multidimensional N=4 SUSY QM to the known exactly integrable
systems and problems of quantum cosmology are briefly discussed.
