Short answers, pulled from the story.
Cornelis Drebbel demonstrated the first compound microscope in London around 1621 and another in Rome in 1624. Historical debate exists regarding the true inventor, with claims ranging from Zacharias Janssen to Hans Lippershey.
Antonie van Leeuwenhoek lived from 1632 to 1724 and brought the microscope to the attention of biologists through his home-made simple microscopes. His devices used a single small yet strong lens that enabled detailed images that compound microscopes could not match for over 150 years.
The maximum resolving power of optical microscopes is typically limited to around 200 nanometers due to the diffraction limit of visible light. This limit arises because point objects appear as fuzzy discs surrounded by diffraction rings known as Airy disks when viewed at very high magnifications.
August Köhler developed Köhler illumination in August 1893 to enhance the quality of images by providing extremely even lighting. This technique overcomes limitations of older illumination methods and is often provided on more expensive instruments.
Eyepieces typically have magnification values including 5x, 10x, 15x, and 20x. Objective lenses range from 5x to 100x with numerical apertures from 0.14 to 0.7, while oil immersion objectives reach magnifications of 40x to 100x.
Eric Betzig, William Moerner, and Stefan Hell won the Nobel Prize in Chemistry in 2014 for their work on super-resolved fluorescence microscopy. Their techniques surpass the diffraction limit and allow for the detection of single molecules.