  The energetic beam of (spin and isospin zero) $\alpha$-particles remains a
very efficient probe for the nuclear isoscalar giant resonances. In the present
work, a microscopic folding model study of the isoscalar giant resonances in
$^{208}$Pb induced by inelastic \aPb scattering at $E_{\rm lab}=240$ and 386
MeV has been performed using the (complex) CDM3Y6 interaction and nuclear
transition densities given by both the collective model and Random Phase
Approximation (RPA) approach. The fractions of energy weighted sum rule around
the main peaks of the isoscalar monopole, dipole and quadrupole giant
resonances were probed in the Distorted Wave Born Approximation analysis of
inelastic \aPb scattering using the double-folded form factors given by
different choices of the nuclear transition densities. The energy distribution
of the $E0, E1$ and $E2$ strengths given by the multipole decomposition
{analyses} of the \aap data under study are compared with those predicted by
the RPA calculation.
