Short answers, pulled from the story.
The first recorded refracting telescope appeared in the Netherlands around 1608, when Hans Lippershey, a spectacle maker from Middelburg, unsuccessfully tried to patent one. Galileo Galilei heard of the invention in May 1609 while in Venice, built his own version, and used it to make astronomical discoveries.
A Galilean telescope uses a concave (plano-concave) eyepiece lens and produces an upright image with no intermediary focus. A Keplerian telescope, invented by Johannes Kepler in 1611, uses a convex eyepiece, which allows a wider field of view and higher magnification but produces an inverted image.
An achromatic refractor uses an objective made of two glass elements, crown glass and flint glass, to bring red and blue light into focus at the same plane, reducing chromatic aberration. Chester Moore Hall invented the achromatic lens in 1733; John Dollond independently invented and patented the same design around 1758.
Refracting telescopes were used to discover the four largest moons of Jupiter (by Galileo in 1609-1610), Saturn's moon Titan (by Christiaan Huygens on the 25th of March 1655), the moons of Mars (Deimos and Phobos, by Asaph Hall in 1877), and Amalthea, a fifth moon of Jupiter (by Edward Emerson Barnard in 1892). The interstellar medium was also first detected using the Great Refractor of Potsdam in 1904.
Refractors are limited by the practical maximum lens diameter of around 1 meter, since gravity causes the center of larger lenses to sag. Glass also absorbs and reflects light, blocking some wavelengths entirely. Reflecting telescopes, which use mirrors instead of lenses, can be built to much larger apertures and have largely replaced refractors for research.
The Great Paris Exhibition Telescope of 1900 had an objective lens 1.25 meters in diameter, making it the largest achromatic refractor ever built. It was dismantled after the exhibition. The Archenhold Observatory houses the longest refracting telescope ever built, with a 68-centimeter aperture and a 21-meter focal length.