His early studies, at the Univ. of Pisa, were in medicine, but he was soon drawn to mathematics and physics. It is said that at the age of 19, in the cathedral of Pisa, he timed the oscillations of a swinging lamp by means of his pulse beats and found the time for each swing to be the same, no matter what the amplitude of the oscillation, thus discovering the isochronal nature of the pendulum, which he verified by experiment. Galileo soon became known through his invention of a hydrostatic balance and his treatise on the center of gravity of solid bodies. While professor (1589–92) at the Univ. of Pisa, he initiated his experiments concerning the laws of bodies in motion, which brought results so contradictory to the accepted teachings of Aristotle that strong antagonism was aroused. He found that bodies do not fall with velocities proportional to their weights, but he did not arrive at the correct conclusion (that the velocity is proportional to time and independent of both weight and density) until perhaps 20 years later. The famous story in which Galileo is said to have dropped weights from the Leaning Tower of Pisa is apocryphal. The actual experiment was performed by Simon Stevin several years before Galileo's work. However, Galileo did find that the path of a projectile is a parabola, and he is credited with conclusions foreshadowing Newton's laws of motion.

In 1592 he began lecturing on mathematics at the Univ. of Padua, where he remained for 18 years. There, in 1609, having heard reports of a simple magnifying instrument put together by a lens-grinder in Holland, he constructed the first known complete astronomical telescope. Exploring the heavens with his new aid, Galileo discovered that the moon, shining with reflected light, had an uneven, mountainous surface and that the Milky Way was made up of numerous separate stars. In 1610 he discovered the four largest satellites of Jupiter, the first satellites of a planet other than Earth to be detected. He observed and studied the oval shape of Saturn (the limitations of his telescope prevented the resolving of Saturn's rings), the phases of Venus, and the spots on the sun. His investigations confirmed his acceptance of the Copernican theory of the solar system; but he did not openly declare a doctrine so opposed to accepted beliefs until 1613, when he issued a work on sunspots. Meanwhile, in 1610, he had gone to Florence as philosopher and mathematician to Cosimo II de' Medici, grand duke of Tuscany, and as mathematician at the Univ. of Pisa.

In 1611 he visited Rome to display the telescope to the papal court. In 1616 the system of Copernicus was denounced as dangerous to faith, and Galileo, summoned to Rome, was warned not to uphold it or teach it. But in 1632 he published a work written for the nonspecialist, Dialogo … sopra i due massimi sistemi del mondo [dialogue on the two chief systems of the world] (tr. 1661; rev. and ed. by Giorgio de Santillana, 1953; new tr. by Stillman Drake, 1953, rev. 1967); that work, which supported the Copernican system as opposed to the Ptolemaic, marked a turning point in scientific and philosophical thought. Again summoned to Rome, he was tried (1633) by the Inquisition and brought to the point of making an abjuration of all beliefs and writings that held the sun to be the central body and the earth a moving body revolving with the other planets about it. Since 1761, accounts of the trial have concluded with the statement that Galileo, as he arose from his knees, exclaimed sotto voce, E pur si muove [nevertheless it does move]. That statement was long considered legendary, but it was discovered written on a portrait of Galileo completed c.1640.

After the Inquisition trial Galileo was sentenced to an enforced residence in Siena. He was later allowed to live in seclusion at Arcetri near Florence, and it is likely that Galileo's statement of defiance was made as he left Siena for Arcetri. In spite of infirmities and, at the last, blindness, Galileo continued the pursuit of scientific truth until his death. His last book, Dialogues Concerning Two New Sciences (tr., 3d ed. 1939, repr. 1952), which contains most of his contributions to physics, appeared in 1638. In 1979 Pope John Paul II asked that the 1633 conviction be annulled. However, since teaching the Copernican theory had been banned in 1616, it was technically possible that a new trial could find Galileo guilty; thus it was suggested that the 1616 prohibition be reversed, and this happened in 1992. The pope concluded that while 17th-century theologians based their decision on the knowledge available to them at the time, they had wronged Galileo by not recognizing the difference between a question relating to scientific investigation and one falling into the realm of doctrine of the faith.