Plano-convex lens: a lens element with one flat surface and the other convex. This element has positive focal length.

Bi-convex lens: a lens element with two convex surfaces of equal radius. This element has positive focal length.

Plano-concave lens: a lens element with one flat surface and the other concave. This lens has negative focal length.

Bi-concave lens: a lens element with two concave surfaces of equal radius.  This element has negative focal length.

Achromatic doublet lens:  a doublet lens free of axial chromatic aberration, 3rd order spherical and coma aberration.

"Best-form" lens:  a single lens element free of 3rd order spherical aberrations for distance object.

Aplanatic meniscus lens: a lens element that increases the relative aperture (or lowering the f/#) of another lens without introducing additional spherical aberrations and coma.