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".
Reflecting telescope
The idea that curved mirrors behave like lenses dates back at least to Alhazen's 11th century treatise on optics, works that had been widely disseminated in Latin translations in early modern Europe. Soon after the invention of the refracting telescope, Galileo, Giovanni Francesco Sagredo, and others, spurred on by their knowledge of the principles of curved mirrors, discussed the idea of building a telescope using a mirror as the image forming objective. There were reports that the Bolognese Cesare Caravaggi had constructed one around 1626 and the Italian professor Niccolò Zucchi, in a later work, wrote that he had experimented with a concave bronze mirror in 1616, but said it did not produce a satisfactory image. The potential advantages of using parabolic mirrors, primarily reduction of spherical aberration with no chromatic aberration, led to many proposed designs for reflecting telescopes. The most notable being James Gregory, who published an innovative design for a ‘reflecting’ telescope in 1663. It would be ten years (1673), before the experimental scientist Robert Hooke was able to build this type of telescope, which became known as the Gregorian telescope.