  The minimal supersymmetric standard model with a low scale see-saw mechanism
is presented. Within this framework, the lepton flavour violation in the
charged lepton sector is thoroughly studied. Special attention is paid to the
individual loop contributions due to the heavy neutrinos $N_{1,2,3}$,
sneutrinos $\tilde{N}_{1,2,3}$ and soft SUSY-breaking terms. For the first
time, the complete set of box diagrams is included, in addition to the photon
and $Z$-boson mediated interactions. The complete set of chiral amplitudes and
their associate form-factors related to the neutrinoless three-body charged
lepton flavor violating decays of the muon and tau, such as $\mu \to eee$,
$\tau \to \mu\mu\mu$, $\tau \to e\mu\mu$ and $\tau \to ee\mu$, as well as the
coherent $\mu \to e$ conversion in nuclei, were derived. The obtained
analytical results are general and can be applied to most of the New Physics
models with charged lepton flavor violation. This systematic analysis has
revealed the existence of two new box form factors, which have not been
considered before in the existing literature in this area of physics.
  In the same model, the systematic study of one-loop contributions to the muon
anomalous magnetic dipole moment $a_\mu$ and the electron electric dipole
moment $d_e$ is performed. Special attention is paid to the effect of the
sneutrino soft SUSY-breaking parameters, $B_\nu$ and $A_\nu$, and their
universal CP phases ($\theta$ and $\phi$) on $a_\mu$ and $d_e$.
