This is essentially the content of a traditional undergraduate course in differential geometry, with clarification of the notions of surface and mapping. For readers with access to a computer containing Mathematica , Maple , or other symbolic computation programs, I have included about 30 optional computer exercises. These are not an essential part of the book but rather an extension of it. Computer skill is not a prerequisite. The appendix contains a summary of the syntaxes of Mathematica and Maple and a list of explicit computer commands covering the basic geometry of curves and surfaces.
Further commands appear in the answers to exercises.
In general we have given simple forms, which readers with computer experience can refine and amplify.