Experimental research of the two-dimensional electron system bound on a liquid helium surface is reviewed. Introductory description is given of the image-potential-induced electronic surface state and of the two-dimensional electron system. Discussion is mainly focused upon the electron correlation effect and the liquid-solid phase transition of the electron system. The experiment by Grimes and Adams, which presented the first experimental evidence for Wigner crystallization of the surface electron system, is explained in detail. Other related experiments are described.