Sidereus Nuncius
The first telescopes appeared in the Netherlands in 1608 when Middelburg spectacle-maker Hans Lippershey tried to obtain a patent on one. By 1609 Galileo had heard about it and built his own improved version. He probably was not the first person to aim the new invention at the night sky but his was the first systematic (and published) study of celestial bodies using one. One of Galileo's first telescopes had 8x to 10x linear magnification and was made out of lenses that he had ground himself. This was increased to 20x linear magnification in the improved telescope he used to make the observations in "Sidereus Nuncius".
Zacharias Janssen
The claim that Zacharias Janssen invented the telescope and the microscope dates back to the year 1655. During that time Dutch diplomat Willem Boreel conducted an investigation trying to figure out who invented the telescope. He had a local magistrate in Middelburg follow up on a 45 year old recollection of a spectacle maker named "Hans" who told a young Boreel in 1610 about inventing the telescope. In his investigation the magistrate was contacted by a then unknown claimant, Middelburg spectacle maker Johannes Zachariassen, the son of Zacharias Janssen, who testified under oath that his father invented the telescope and the microscope as early as 1590 and that Hans Lippershey had stolen his father's invention of the telescope. This testimony seemed to convincing to Boreel, who modified his recollections, concluding that Zacharias must have been who he remembered. Boreel's conclusion that Zacharias Janssen invented the telescope a little ahead of spectacle maker Hans Lippershey was adopted by Pierre Borel in his 1656 book on the subject.