We describe surfaces and geodesics without assuming
prior knowledge of differential geometry. This involves selecting and
presenting basic definitions and theorems. Included in this
discussion are definitions of surface, coordinate patch, curvature,
geodesic, etc. This summary closes with a proof of the
length-minimizing properties of geodesics. Examples of surfaces of
constant gaussian curvature are given and plotted in Mathematica.
We also describe geodesics on these surfaces and plot select
examples.