Quadrics
Quadrics surfaces are surfaces in R3 defined by quadratic equations in the coordinates. There are 5 types of non-degenerate quadric surfaces, illustrated below.
The images coming in pairs side by side are stereographic: look at the left one with your right eye and vice versa to see the surface in three dimensions.
Ellipsoid
Elliptic paraboloid
Hyperbolid paraboloid
One-sheeted hyperboloid
Two-sheeted hyperboloid