What discoveries did Galileo make using a telescope

He discovered that the Earth wasn't the center of the solar system and that the sun was. He argued that if the Earth was the center of the solar system, Jupiter's moons would be orbiting around Earth and not Jupiter.

His most important discovery was that the Earth was not at the center of the universe, contrary to what the Catholic Church had been teaching. He also discovered the phases of Venus, Jupiter's four moons, and the rings of Saturn. He found that the moon was its own world, with its own craters and valleys and such. Basically, he discovered that the Earth wasn't that special in comparison with everything else in the Universe. The Church didn't like this. Galileo was charged with heresy. He was put on house arrest for the rest of his life, locked in a chapel, and made to listen to scripture.