What is the difference between a binocular, trinocular, and stereo microscope?

In a binocular microscope, there is one optical path originating from the microscope objective. The optical path is then split into two paths that are then brought each eye. If your microscope has two eyepieces, but one objective, then chances are it is a binocular microscope. A trinocular microscope works the same way, but the optical path is split into three paths- two for your eyes and a third port usually for a camera connection. In a stereo microscope, there are two paths originating from the microscope objective that travel essentially parallel up to the eyepieces. The advantage of using a stereo microscope over a binocular microscope is in the depth perception. Having two separate optical paths makes depth perception and three-dimensional viewing of an object possible. Using a binocular microscope, you will see only a flat field and will not be able to discern any height differences on the object that you are viewing.