The microscope illuminator and condenser are designed to illuminate a transparent sample with transmitted light.

Absorption of light generates the contrast that we see; either by selective wavelength absorption (imparting color) or by intensity attenuation.

Edmund Culpeper (1670–1738) was the first to place a mirror under the sample so that light would be transmitted through the specimen. This is a late Culpeper compound microscope from about 1730.
A few years later, opticians added a second reflecting surface to the illuminating mirror. This surface was concave, which provided a higher quality, focused light on the sample.
This is a mirror on a Benjamin Martin microscope from around 1775. One surface is flat, and the other is curved.
Until late in the 19th Century, samples were illuminated only by light reflected by a flat or concave mirror.
In the late 1800s, Edward Milles Nelson invented a lensed device that presented a focused beam of illuminating light onto the sample. This device is known as the Substage Condenser. The illumination method is called Critical Illumination. Nelson designed microscopes for the Powell & Lealand microscope company. Left is an example of a Powell & Lealand instrument with a Critical Illuminating substage condenser. The microscope is from c1868.
The latest advance in sample illumination was invented by August Köhler in 1893 for the Zeiss microscope company. The example shown here is a 1905 Leica microscope equipped with a Köhler illuminating condenser. Köhler Illumination
Critical Illumination