[en] First we present the covariantly quantized space-time supersymmetric superstring. The main ingredients are additional auxiliary variables and their corresponding auxiliary gauge symmetries. They allow a Lorentz covariant gauge fixed lagrangian path integral which has the form of a free 2-dimensional conformal field theory with a finite number of 2-dimensional world-sheet fields and ghosts. Next we show that the path integral is anomaly free in 10 space-time dimensions. Then, by a canonical (operator) quantization we obtain in the point-particle limit the covariant equations of motion of the D=10 super Yang-Mills (SYM) theory. (authors)