The heavy quarkonium states consist of a quark and an anti-quark. The first heavy quarkonium states discovered in the early seventies of the last century were the charmonium states consisting of c quark and antiquark. Later, the bottomonium states consisting of b quark and antiquark were discovered. In the last decade of the last century, the mesons consisting of b quark and antiquark was also discovered. The top quark has a very short lifetime and does not form bound states. These states of heavy quarkonium helped us understand many features of the theory of quantum Chromodynamics (QCD) which describe the interactions between quarks and gluons. However, since the theory of QCD proved to be very difficult to solve, many models were proposed to explain the spectrum of the heavy quarkonium states, the decays of these states, and the transitions between their excited states. In this thesis we have used a quarkonium model with Hulthen potential describing the short range interaction to calculate various decays of heavy quarkonium states. We have calculated the decay constants, the leptonic decay widths, two photons widths, two gluon widths, and also radiative decays of electric dipole and magnetic dipole types. We have compared our results with experimental results and also with the results of other relevant models. We conclude that this model gives a good description of the decay properties of the heavy quarkonium states...