|The 1610 “telescope” (top) built by Galileo, a 30x power telescope, based on the reports of the telescope devised by Hans Lippershey (1608). |
In 1289, an anonymous Florentine manuscript referred to “glass lenses for spectacles recently invented, of great advantage to old people with weak vision”. 
In c.1500, Leonardo da Vinci, in his note books, jotted the following note to self in respect to making some type of telescope, which he had in mind:
“Make glasses to see the moon large.”— Leonardo da Vinci (c.1500), Notebooks 
In c.1515, Pope Leo X is reported to have used some type of instrument to observe, from the Medici Palace in Florence, “distant hunting chases and birds flying over the Fiesole hills”. 
In 1538, Girolamo Fracastoro (1478-1553) (Ѻ), an Italian physician, had the idea of using two convex lenses, placed one of top of the other, so to see the moon or a star, like one sees a far-away steeple:
“If anyone looks through two spectacle lenses, one placed on top of the other, he will see everything much larger and closer. Indeed, certain spectacle lenses are made of such density, that if someone looks through them at the moon or at another star, he will judge than to be so close that they do not even appear to exceed the steeples themselves [in height]. This is why one should not be surprised if the same also occurs through the parts of the [heavenly] orbs?”— Girolamo Fracastoro (1538), Person-Centric: Of the Stars 
In c.1550, Leonard Digges (c.1515-c.1559) (Ѻ), an English mathematician and surveyor, as reported by his son Thomas Digges, in his Pantometria (1571), is said to invented a “proportional glass” to view distant objects:
“By proportional Glasses duly situate in convenient angles, not only discovered things far off, read letters, numbered pieces of money with the very coin and superscription thereof, cast by some of his friends of purpose upon downs in open fields, but also seven miles off declared what hath been done at that instant in private places.”— Thomas Digges (1571), Pantometria 
In 1580s, Giovanni Porta began to discuss his work with multiple lenses employed to see far:
“I have made glasses that can recognize a man several miles away.”— Giovanni Porta (1586), “Letter” 
“The figures hovering clearly and plainly as if I see my hands.”— Giovanni Porta (1593), The Refraction 
In 1589, Porta, in his Natural Magic (§10), spoke of a “a combination of concave and convex lenses for improving long-distance vision.” 
In 1608, Hans Lipperhey, a German-born Dutch spectacle maker, through some type of special order package for an unnamed customer, invented the telescope, or “Dutch perspective glass” as it later came to be called, and the tried to obtain a patient for it; the following is one account of this event:
“In the year 1609 [sic], there appeared a genius or some other man, as yet unknown, of the race of Hollanders, who, in Middleburg in Zeeland, visited Johannes Lippersein, a man distinguished from others by his remarkable appearance, and a spectacle-maker. There is no other [spectacle-maker] in that city, and he ordered many lenses to be made, concave as well as convex. On the agreed day he returned, eager for the finished work, and as soon as he had them before him, raising two of them up, namely a concave and a convex one, he put the one and the other before his eye and slowly moved them to and fro, either to test the gathering point or the workmanship, and after that he left, having paid the maker. The artisan, by no means devoid of ingenuity, and curious about the novelty, began to do the same and to imitate the customer, and quickly his wit suggested that these lenses should be joined together in a tube. And as soon as he had completed one, he rushed to the court of Prince Maurice and showed hint the invention. The prince had one [or, had been acquainted with one] before, and lest it should be suspected that [the device] was of military value, and very necessary, had kept it a secret. But now that he found by chance that it had become known he disguised [his prior knowledge], rewarding the industry and good intentions of the artisan.”— Giovanni Sirtori (1612), Publication 
On 7 Jan 1610, news of Lippershey’s telescope invention reached Galileo, who built a new improved 30x power telescope, shown above.  Galileo used his telescope to get a closer view of Jupiter, and found three small, bright stars near the planet (Ѻ); that year, he published a small book titled The Starry Messenger describing his findings.
In 1611, Johannes Kepler, in his Dioptrice, described a system of lenses where the concave eye-piece was replaced by a convex eye-piece. 
1. Ilardi, Vincent. (2007). Renaissance Vision from Spectacles to Telescopes (pg. 208). Publisher.
2. Gonzalez, Karina; Burch, Chante R. (2014). “Physical Sciences: Elementary Physics – Telescopes, Mankind’s Eye into the Universe” (Ѻ), Salt Lake City Community College, Physics 1010, Fall.
3. (a) Fracastoro, Girolamo. (1538). Person-Centric: Of the Stars (Homocentricorum sive de stellis liber unus). Publisher.
(b) Telescopes – Bo.Astro.it.
(c) Ilardi, Vincent. (2007). Renaissance Vision from Spectacles to Telescopes (pg. 208). Publisher.
4. Telescopes – Bo.Astro.it.
● Telescope – Wikipedia.