In this paper, we describe the main principles of our approach for the visualization of surfaces and curves on them in three-dimensional space by the use of line graphics. We also compare our approach with the standard method of polygon mesh. Mainly, we discuss the representation of surfaces, special lines on surfaces and lines of intersections of surfaces. Furthermore, we address the problems of visibility and finding the contour lines of surfaces. Finally we apply our method for visualizing some selected topic in mathematics.