Galileo made some very important discoveries in Astronomy which directly opposes the Aristotlean Astronomy and Ptolemic Theory (which is also based on Aristotlean principles).He made the extensive use of his newly discovered telescope observing the night sky.This important discoveries were first published in his book Siderus Nuncius (1610) or The Starry Messanger in English.
According to Aristotle the Moon and other heavenly bodies are made of quintessence which never changes and they are perfectly spherical in shape.But Galileo with his telescope observed that Moon has craters and mountains on its surface.
He also observed that four satellites are revolving around Jupiter.It also opposes Aristotle as according to him everything in the universe should rotate around the Earth.