The astronomers we have considered thus far, although they may differ among themselves, are all followers of the methods of mathematical astronomy descending from Ptolemy’s Almagest. Galileo, while knowledgeable in these methods, was led to his original contributions to astronomy through a search for physical or mechanical descriptions of phenomena on the earth, through his discoveries of the nature of the heavens revealed by the telescope, and through his criticism of Aristotelian natural philosophy, both of the heavens and of the earth, based upon his discoveries with the telescope and in mechanics. For someone who cannot strictly be called an astronomer, at least not in the traditional sense, astronomy occupied a preeminent part of Galileo’s work, from his first teaching to his last observations of the moon just before he lost his sight, and he wrote more on astronomy than on all other subjects. His most important work was concerned with two issues: the refutation of the Aristotelian and the defense of the Copernican “System of the World,” and what he did above all was think, for no one could think as quickly and as ingeniously as Galileo. And no one could think as originally, no one was as free of the past. No one, not even Kepler, contributed more to the establishment of Copernican theory, and in a history that will live forever, no one suffered more for his trouble.