The basic tool that Galileo used was a crude refracting telescope. His initial version only magnified 8x but was soon refined to the 20x magnification he used for his observations for Sidereus nuncius. It had a convex objective lens and a concave eyepiece in a long tube. The main problem with his telescopes was their very narrow field of view, typically about half the width of the Moon.
The science of astronomy took a huge leap forward in the first decade of the 1600s with the invention of the optical telescope and its use to study the night sky. Galileo Galilei did not invent the telescope but was the first to use it systematically to observe celestial objects and record his discoveries. His book, Sidereus nuncius or The Starry Messenger was first published in 1610 and made him famous. In it he reported on his observations of the Moon, Jupiter and the Milky Way. These and subsequent observations and his interpretations of them eventually led to the demise of the geocentric Ptolemaic model of the universe and the adoption of a heliocentric model as proposed in 1543 by Copernicus.