Invention of the Telescope
It is a popular misconception that Galileo Galilei invented the telescope. While Galileo is largely responsible for turning the telescope into an astronomical instrument, the telescope was not his original invention.
The actual invention of the telescope is shrouded in the murky fog of history, with some claims going back hundreds of years before Galileo.
Early 1600's Netherlands
The credit for the modern invention of the telescope is typically given to a Dutch optician named Hans Lippershea. In 1608, Lippershea applied for a patent on his device. His application preceded that of another dutchman, Jacob Metius, by a few weeks. Both patents were, however, rejected. The patents were rejected as the concept appeared to already be well-established and, therefore, the invention was not deemed worthy of patent.
In 1655, William de Boreel investigated the history of the telescope and, based on the claim if Johannes Zachariassen that his father, Zacharias Janssen, invented the instrument as early as 1590, determined this was the true inventor. However this is entirely based on Zachariassen's claim, and he is therefore typically not credited with the invention.
What appears fairly certain, however, is that the inventions of Lippershea, and, possibly, to a lesser extent Metius, were what lead to the popularization of and advances in the design of the modern telescope. While both patents were refused, both received commissions from the Hague to manufacture more examples of their design, which began to proliferate through the region.
In 1609, Jaqcques Bovedere, a French scientist, appears to have been introduced to the device in Paris. Bouvedere was an associate of Galileo's and apparently described the instrument to the Italian scientist, who then, based on the descriptions, set out to construct his own.
It is fair, then, to say that Galileo designed and built his own instruments, and most likely some of his improvements became part of the designs that proliferated around Europe.