The Skyrme model of nuclear physics requires quantization if it is to match
observed nuclear properties. The computation of the normal mode spectra of
multi-Skyrmion solutions isa crucial first step toward this goal. Results
for baryon number B = 2, 3, and 4 Skyrme solitons are presented here. All t
hree spectra possess the same remarkable structure, with the lowest energy
modes lying in those representations expected from an approximate correspon
dence between Skyrmions and BPS monopoles. In each case, the next mode up i
s the "breather", and above that lie higher multipole breathing modes.