Microscopic theory of collective excitations of a quantum dot in a str
ong magnetic field is proposed. A complete analysis of diagrams in the
perturbation theory over the Coulomb interaction is performed. The sp
ectrum of low-lying excitations is calculated for the case of a parabo
lic quantum dot. It is shown to consist of three terms: single-particl
e drift, magnetoplasma and exciton ones, with the exciton term dominat
ing the magnetoplasma one. In the framework of the semi-classical appr
oach, the case of a non-parabolic quantum dot is also discussed. The e
xperimental manifestations of the effects under investigation are disc
ussed.