The purpose of this article is to show the advantage of using *Mathematica* in the theory of surfaces. The examples in the classical differential geometry, namely the theory of curves and surfaces,
have been confined to a small group of calculable objects, because of the difficulty in evaluating geometrical quantities
and solving differential equations explicitly. But *Mathematica* has made it possible to deal with a wide range of objects and to perform experimental treatments of them, based on the power
of numerical calculation--the `NDSolve`

and `NIntegrate`

commands in particular--and graphical visualization by the `ParametricPlot`

command. I would like to introduce here several animations and figures that I use in my differential geometry class for undergraduate
students. First of all, these graphics help students understand the basic notions of differential geometry. Secondly, we can
experiment on geometry through these graphics. This article is one of the serial talks given by the author at 1995 Developer
Conference, *IMS* '97 in Rovaniemi, and WMC 98 in Chicago. They are all targeted for the experimental usage of *Mathematica* on differential geometry. This time the topics are focused on the surfaces in the three-dimensional Euclidean space. The
commands are contained in six notebooks. If the commands in other notebooks cause any trouble, please restart *Mathematica*. See also the explanation of the notebooks.