


The catenoid.
Discovered by L. Euler in 1740. The original name was
allyside. The name catenoid is due to Plateau. 
The helicoid.
Discovered by Meusnieur in 1776. Catalan
characterized it as the only ruled nonflat minimal surface. The next
minimal surface with helicoidal ends was discovered by Hoffman,
Karcher and Wei 220 years later. 
Scherk's
surfaces. In
1835, H. F. Scherk discovered 5 new minimal surfaces using a general
representation for minimal surfaces by Monge. 



Enneper's
surface. Constructed by Enneper in 1863, using his
own representation formulae. 
A singly
periodic surface by Riemann. Riemann
constructed a oneparametric family of properly
embedded minimal surfaces, {R_{l} : l
>0 }, which are invariant under a translation. This picture
corresponds to R_{1}. 
Schwarz'
P surpace. The
fundamental region is a tetrahedron which is 1/48 of a cube. The surface
divides space into two congruent labyrinths. 



ChenGackstatter
surfaces. The first known examples with finite total
curvature and genus greater than zero. 
Costa's
surface. Constructed by C. Costa in 1981.
Hoffman and Meeks gave the first proof of its embeddedness. It has the
topology of a compact torus minus three points. 
