Surfaces in 3-dimensional Space

This chapter is an introduction to the local properties of the surfaces in 3-dimensional space. Before coming to (necessarily) heavy definitions, I give a few simple examples of objects which I am sure the reader will agree should be called surfaces: surfaces of revolution, ruled surfaces, etc. I then come to the definitions and to the affine properties, tangent plane and position with respect to the tangent plane, in particular. The last section is devoted to the metric properties of surfaces in a Euclidean space, in particular to the Gauss curvature.