Some of the models illustrate quite straightforward mathematical ideas, which should be accessible to anybody who has studied calculus at the level of Further Mathematics A-level. The quadric surfaces are one example. More advanced ideas are also illustrated in these models, and especially in the more complex ones such as cubic surfaces. One relatively easy concept is that of a  ruled surface, which you can think of as being generated by moving a straight line around in space. For other surfaces, it is important to understand some basic concepts, such as singularities, from algebraic geometry, along with ideas such as curvature and geodesics from differential geometry. The links on the left give a starting point, and links to more advanced resources.