His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism, that's why he is well known for having dared to defy the Roman Catholic Church by agreeing with the theory, formulated in 1512 by the Polish astronomer Nicholaus Copernicus (1473-1543), that the planets including Earth orbited the Sun. In that time it was believed by the Church that the Earth was the center of the Universe and all the stars (including our own Sun) were orbiting around our planet - as their movement can be seen on the sky. He paid for his heresy by spending the last eight years of his life under virtual house arrest.
From scientific and historical point of view, Galileo Galilei has been called the father of modern observational astronomy, the father of modern physics, the father of science and the Father of Modern Science because of his role in the development of astronomy and science... However, what is less well known is that it was the tool he used in his researches, as much as the conclusions he came to, that got him into trouble with the Church and the Inquisition.
In 1512 Nicholaus Copernicus had come to his conclusions on purely theoretical grounds, but without making any direct observations of the motions of the planets. Even had he wished to do so he would have been very limited in what he could see, because the first practical telescope is believed to have been developed by Hans Lippershey, a lens maker of Middleburg in the Netherlands, in 1608. However, it is not known who first discovered that if one looked through two lenses, one concave and one convex, distant objects appeared to be much closer. In 1609 Galileo Galilei was, along with Englishman Thomas Harriot and others, among the first to use a refracting telescope as an instrument to observe stars, planets or moons. The name "telescope" was coined for Galileo's instrument by a Greek mathematician, Giovanni Demisiani in 1611: the name was derived from the Greek tele = 'far' and skopein = 'to look or see'. In 1610 he used a telescope at close range to magnify the parts of insects and by 1624 Galileo had perfected a compound microscope.
In that years he did make a number of significant improvements in telescope design - he was able to increase its power of magnification from 3x to 30x very soon after first experimenting with a Lippershey instrument.
What was called the Galileo affair was a sequence of events that began around 1610, during which Galileo Galilei came into conflict with the Catholic Church over his support of Copernican astronomy. In 1610 he published his Sidereus Nuncius (Starry Messenger), describing the surprising observations that he had made with the new telescope, namely the phases of Venus and the Galilean moons of Jupiter. He went on to propose a theory of tides in 1616 (as the evidence for the motion of the Earth), and of comets in 1619, and promoted the heliocentric theory of Copernicus (published in De revolutionibus orbium coelestium in 1543).
However, there was a problem when it came to dealing with the Church, in terms of demonstrating his discoveries. In time of Galilei it was acceptable to wear lenses as spectacles because that was only restoring one’s sight to the level that God had given one, but the telescope went much further than that: ordinary people were capable to see that they were not supposed to, more than God intended. Only God was all seeing, and watching the skies and seeking to emulate God in this respect was a heresy. Therewere many people at the time who refused to look through a telescope, in the belief that they would commit a sin by so doing.
Because Galileo Galilei was committing a heresy by supporting the Copernican view of the solar system ans he was using an instrument of the Devil, the telescope, he was called by the Inquisition in Rome to recant the views expressed in his Dialogue Concerning the Two Chief World Systems.
A few years earlier, in 1600, Giordano Bruno was burned at the stake for his views about astronomy: he dared to say that the Sun was just another star in the sky. In the case of Galileo Galilei, his part in the controversies over theology, astronomy, and philosophy culminated in his trial by the Roman Inquisition in 1633 who found him "gravely suspect of heresy" and sentenced him to indefinite imprisonment. Galilei was banned from publishing any further works... He spent his remaining years summarising his earlier work while in house arrest, under which he remained for the rest of his life.