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".
Thomas Harriot
Halley's Comet in 1607 turned Harriot's attention towards astronomy. In early 1609 he bought a "Dutch trunke" (telescope), invented in 1608, and his observations were among the first uses of a telescope for astronomy. Harriot is now credited as the first astronomer to draw an astronomical object after viewing it through a telescope: he drew a map of the Moon on 26 July 1609, preceding Galileo by several months. He also observed sunspots in December 1610.