Multiple Coulomb excitation with heavy-ion beams offers an unique opportuni
ty to study model-independently the collective properties of the nuclear st
ructure. Existing detector systems and data analysis methods allow not only
to measure complete sets of parameters describing the electromagnetic prop
erties of the nuclei - electric and magnetic multipole matrix elements - bu
t also by using sum rules to translate these results to the shape evolution
of the charge distributions independently for each level. The technique of
Coulomb excitation can also be used to answer specific questions, as illus
trated in this paper.