After 1609 - Galileo Galilei is described as being able to close focus his telescope to view small objects close up and/or looking through the wrong end in reverse to magnify small objects. A telescope used in this fashion is the same as a compound microscope but historians debate whether Galileo was magnifying small objects or viewing near by objects with his terrestrial telescope (convex objective/concave eyepiece) reversed.
1619 - Earliest recorded description of a compound microscope, Dutch Ambassador Willem Boreel sees one in London in the possession of Dutch inventor Cornelius Drebbel, an instrument about eighteen inches long, two inches in diameter, and supported on 3 brass dolphins.
1621 - Cornelius Drebbel presents, in London, a compound microscope with a convex objective and a convex eyepiece (a "Keplerian" microscope).
1625 - Giovanni Faber of Bamberg (1574 - 1629) of the Linceans, after seeing Galileo's occhiolino, coins the word microscope by analogy with telescope.
1655 - In an investigation by Willem Boreel, Dutch spectacle-maker Johannes Zachariassen claims his father, Zacharias Jansen, invented the compound microscope in 1590. Zachariassen's claimed dates are so early it is sometimes assumed, for the claim to be true, that his grandfather, Hans Martens, must have invented it. Findings are published by writer Pierre Borel. Discrepancies in Boreel's investigation and Zachariassen's testimony (including misrepresenting his date of birth and role in the invention) has led some historians to consider this claim dubious.
1665 - Robert Hooke publishes Micrographia, a collection of biological micrographs. He coins the word cell for the structures he discovers in cork bark.
1863 - Henry Clifton Sorby develops a metallurgical microscope to observe structure of meteorites.
1860s - Ernst Abbe discovers the Abbe sine condition, a breakthrough in microscope design, which until then was largely based on trial and error. The company of Carl Zeiss exploited this discovery and becomes the dominant microscope manufacturer of its era.