The Stokes wave is the fully nonlinear periodic gravity wave on a surface of a fluid parameterized by its height. The wave of greatest height has the limiting form with 120 degrees angle on the crest as found by Stokes in 1880. The wave is fully characterized by the complex singularities in the upper complex half-plane of a conformal map of a free fluid surface into the real line, with the fluid domain mapped into the lower complex half-plane. The only singularity in the physical sheet of Riemann surface of non-limiting wave is the square-root branch point located on the imaginary axis. The second sheet has a singularity in lower complex half-plane. We found the infinite number of square root singularities in infinite number of non-physical sheets of Riemann surface. As the height of the Stokes wave increases, all these singularities simultaneously approach the real line from different sheets of Riemann surface and merge together forming 2/3 power law singularity of the limiting wave.