Premelting means that the surface of a material melts at a temperature below the bulk melting temperature. This phenomenon is not universal and depends on the material. Until now, premelting was detected by measuring the temperature dependence of the crystallographic structure of the surface. Most of these measurements showed gradual increase of the thickness of the premelted layer. Melting is usually accompanied by the vanishing of the shear modulus, a latent heat and a jump of the density. In this work, we made the first observation of premelting of gallium by measuring the shear modulus of the surface. Premelting begins at T=294K while the bulk melting temperature is 303K. Well below premelting, the surface shear modulus is the same as the bulk shear modulus. It decreases continuously, and vanishes at surface melting temperature (294K). For comparison, bulk shear modulus vanishes discontinuously at the bulk melting temperature (303K). Our results are consistent with premelting detected in crystal structure measurements at the surface of a single crystal gallium. In that measurement, the surface starts to melt at 294K. In our work, we also observe optically the dynamics of surface melting and see the propagation of morphological changes at the surface