Optical
From the jeweler's loupe and the handheld magnifying glass to the compound microscope using multiple lenses, the most familiar enlarging instrument is the optical, or light, microscope, magnifying from 3X up to 2,000X original size.
Inverted
Usually used for looking at cell cultures in biology applications or in medical study, this scope is turned upside down with the light source at the top and eyepieces pointed up.
Stereoscopic
A stereoscopic microscope is a twin set of scopes set up alongside each other, giving a binocular effect. Each eye sees the image independently allowing for the observation of relief in the subject. These can be found in microsurgery operations or fine tool adjustment work and are also used in the electronics field, allowing workers to check leads on circuitry.
Polarizing
Polarizing microscopes are used in geology to study crystal formations and have been used extensively in detecting asbestos fibers.
Metallographic
If there are flaws in metal surfaces, metallographic scopes will detect them. They're also used to study crystal structures in metal alloys and examine minerals and rocks, and are applied in forensic investigation.
Phase-Contrast
Sometimes objects being magnified are nearly transparent and get lost in the medium they're mounted in. Cell nuclei are an example. Shifting, or phasing, the light source through the object helps to provide an image because the cell structure of the object is different than the medium.