  We study lepton flavor observables in the Standard Model (SM) extended with
all dimension-$6$ operators which are invariant under the SM gauge group. We
calculate the complete one-loop predictions to the radiative lepton decays
$\mu\to e\gamma$, $\tau \to \mu \gamma$ and $\tau\to e\gamma$ as well as to the
closely related anomalous magnetic moments and electric dipole moments of
charged leptons, taking into account all dimension-$6$ operators which can
generate lepton flavor violation. Also the 3-body flavor violating charged
lepton decays $\tau^\pm \to \mu^\pm \mu^+ \mu^-$, $\tau^\pm\to e^\pm e^+ e^- $,
$\tau^\pm \to e^\pm \mu^+ \mu^- $, $\tau^\pm \to \mu^\pm e^+ e^- $, $\tau^\pm
\to e^\mp \mu^\pm \mu^\pm$, $\tau^\pm \to \mu^\mp e^\pm e^\pm $ and $\mu^\pm
\to e^\pm e^+ e^-$ and the $Z^0$ decays $Z^0\to\ell_i^+\ell_j^-$ are
considered, taking into account all tree-level contributions.
