What is a quaternary mirror and why does the E-ELT need one?
You may know that a standard Newtonian telescope has two mirrors, they are called the primary and secondary mirror.
The E-ELT has five mirrors: The quaternary mirror is simply &quot;mirror number four&quot;, counting in the direction the light enters the scope.
It's complex because that's where the adaptive optics sits:

The quaternary mirror has an approximate diameter of 2.4-m (2380x2340mm). It is a flat adaptive mirror, with up to 8000 actuators, thereby allowing the surface to be readjusted at very high time frequencies. [...]
This mirror will correct in real time for high order wavefront errors (e.g. atmosphere, wind shake, low spatial frequency telescope errors) and small amplitude residual tip-tilt corrections.

Source: The European Southern Observatory's page on the E-ELT optics