The invention of the telescope and microscope are usually cited as being around the early 1600s.

But sophisticated lenses, easily accurate enough for use in such instruments were being made far earlier. It seems highly unlikely that during a period of at least 500 years, no-one would have thought of putting two or more lenses together to form an optical instrument of some kind - leaving the 1600 dates as questionable.

The invention of the refractive (i,e, lens-based) telescope is usually cited as 1608, when Dutch inventor Hans Lippershey, who made spectacles, applied for a patent.

From then onwards, well-documented development spread rapidly across Europe.

The invention of the compound (i.e. many lenses) microscope is normally cited as c.1620.

The earliest known examples of compound microscopes, which combine an objective lens near the specimen with an eyepiece to view a real image, appeared in Europe around 1620.The inventor is unknown, even though many claims have been made over the years."

Source : Wikipedia

The so-called Visby Lenses are a set of quartz lenses found in several Viking graves on the island of Gotland, Sweden. They have been dated to the 11th or 12th century. The processing of rock crystal was evidently quite common at that time.

They have been accurately ground in such a way as to avoid 'spherical aberration' (severe optical distortions inherent in ball-like lenses), although the mathematical reasons for this would have been unknown at the time. It's thought that the makers used 'trial and error' methods to improve the lenses optical properties.

The shape of the lenses` surface show only minor departures from rotational symmetry. This leads to the conclusion that they were manufactured on some kind of turning-lathe. The surfaces are almost perfectly elliptic."

Source : The Visby Lenses Optometry & Vision Science. 76 (9): 624–630. (archived). (with photos).