Abstract
The purpose of this paper is to draw the concrete surface by the fundamental theorem of surface in R3. There are two chapters in the thesis. In the first, we use the computer to draw a regular surface with the given first and second fundamental forms by the fundamental theorem of surface in . In the second chapter, we connect the Sine –Gordon equation (SGE) with the fundamental theorem of surface. I t means that if a solution of the SGE is given, locally, we may draw a regular surface with Gaussian curvature K= -1, and its fundamental forms can be computed by this solution.