Galileo was born on the 15th Feb 1564, and died on the 8th Jan 1642. He built his first telescopes in 1609, after he had heard details of the device that had been built in the Netherlands in the previous year. Hans Lippershey first applied for a patent to the States-General of the Netherlands on October 2, 1608. There is evidence that the very first telescope was built by Leonard Digges as early as the middle of the 16th century, before Galileo was born. Galileo made a number of improvements to the telescope, including the ability to see upright images; this became what we call the terrestrial telescope. In fact, he had a profitable trade in selling the telescopes he made. When Kepler produced improved telescopes with larger magnification, but inverted images, Galileo kept to his terrestrial design. In 1586, he wrote his first scientific book "The Little Balance" where he describes Archimedes' method of determining specific gravity using a balance.
During June of 1610, he observed four objects, invisible to the naked eye, that appeared to orbit Jupiter. He had discovered the four largest satellites of Jupiter. Subsequently, these became known as the Galilean moons. Later, in September of 1610, he demonstrated that Venus had phases like the moon. This was a huge blow to the geocentric model as it would be impossible for Venus to show all the phases if it, like the sun, orbited the Earth. Observing Saturn, he saw the rings, but his telescope rendered them as two lobes on either side of the planet. He saw that periodically, they disappeared, but this was when the rings were edge on to the view from Earth.
He was also one of the first people to make detailed observations of sunspots. These had been interpreted as being transits of the sun by the planet Mercury, whose orbit around the Earth was determined to be inside the Sun's orbit in the geocentric model. It was difficult for people in those days to overcome the conviction that the sun was perfect, so many would not believe that sunspots could be "flaws" in the Sun's perfection. Furthermore, on turning his telescope to the Milky Way, he determined that it comprised a multitude of individual stars, and not a huge band of nebulosity, as was thought at the time.
Although the story of his dropping weights from the Leaning Tower of Pisa is largely apocryphal, he did study the motion of objects under constant acceleration by rolling balls of various weight down inclines. He proposed that moving objects continue to move uniformly unless a force, friction for example, slows them. Again, this directly contradicted Aristotelian ideas that objects slow down and stop naturally unless a force is applied to maintain their motion. Newton included this principle in his first law of motion.
A truly remarkable fact is that in 1632, he proposed a very early form of relativity that stated "the fundamental laws of physics are the same in all inertial frames". Newton, in fact, advanced this idea, and it was taken up, subsequently, by Einstein as one of the keystones of special relativity.