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".
Radio telescope
Radio waves from space were first detected by engineer Karl Guthe Jansky in 1932 at Bell Telephone Laboratories in Holmdel, New Jersey using an antenna built to study noise in radio receivers. The first purpose-built radio telescope was a 9-meter parabolic dish constructed by radio amateur Grote Reber in his back yard in Wheaton, Illinois in 1937. The sky survey he did with it is often considered the beginning of the field of radio astronomy.