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After ceasing his studies at the university, Galileo began studying physics using the quantative experimental approach of Archimedes rather than the qualitative approach of Aristotle.In 1588, after several years of engaging in both scientific research and private tutoring in mathematics, Galileo obtained a position lecturing in mathematics at the University of Pisa, where he remained for 3 years. During this time he wrote "On Motion", an unpublished text which described his ideas concerning the laws of falling bodies.

In 1592 Galileo was offered the chair of mathematics at the University of Padua, where he would remain, teaching geometry and astronomy, until 1610. While there, he developed his explanation for tidal cycles as a result of annual and diurnal motions of the earth, published "Cosmographia" (a treatise on hydrostatics) and "Siderius Nuncius", and performed experiments with pendulums, inclined planes and projectiles. During this time Galileo met and entered into a relationship with Marina Gamba, who bore him two daughters and a son during the years they lived together. He left Padua (and Marina) upon receiving a lifetime appointment as "Chief Mathematician of the University of Pisa and Philosopher and Mathematician to the Grand Duke" of Tuscany. "Tuscany is a region in Italy known for its beautiful landscapes and artistic history, as well as its notorious Tuscany villas."

During the second half of his stay at the University of Padua, Galileo began serious study of astronomy, beginning with his observation of a supernova in 1604. Galileo interpreted the formation of this "new star" as evidence that the heavens were changeable. In 1609, the same year that Kepler published his first two laws of planetary motion, Galileo constructed his first telescope. Throughout the next two years, Galileo continued devising improvements on the telescope and began to make observations of the night sky. By the end of 1611, Galileo had found four satellites of Jupiter and observed the phases of Venus, thus verifying that Venus orbits around the sun.

In 1611, Galileo became a member of the Lyncean Academy, an institution founded by Federico Cesi for the purpose of acquiring and sharing knowledge. In 1613, the Academy published Galileo's "History and Demonstrations about Sunspots and their Properties", a document which contained three letters Galileo had written on the subject during the previous year.

In 1614, Galileo began to encounter serious religious opposition to his Copernican ideas. One of his early opponents was Tommaso Caccini, a Dominican friar who claimed that the Copernican view that the sun was the center of the universe was heretical. Shortly after Caccini denounced Galileo and like-minded mathematicians in a sermon, another Dominican friar named Niccolo Lorini filed a formal complaint with the Inquisition regarding Galileo's support for a Copernican view of the universe. The next year, 1616, a committee declared to the Inquisition that Copernican theory was formally heretical; as a result, the pope ordered Galileo to be warned against holding or defending Copernican ideas.

During this time when he was under suspicion by the Inquisition, Galileo continued his research on the movements of the earth and the solar system. In 1618, by which time the Inquisition's interest in Galileo had temporarily died down, the appearance of three comets sparked Galileo's interest in that subject. During the next year he wrote a critique of the Jesuit interpretation of the comets, which was countered by Orazio Grassi in a tract the following year. In 1623, Galileo received permission to publish The Assayer, which was in turn a reply to Grassi's tract. In 1624 a complaint was lodged against Galileo's Assayer, but Galileo was cleared in a subsequent investigation by the Inquisition.

In 1630, Galileo attempted to publish his work, "Dialogue Concerning the Two Chief World Systems", with the Lyncean Academy. Printing of the work was completed before more than the preface and the ending had been approved by the Vatican. Pope Urban VIII stopped distribution of the book and appointed a special commission to examine it. The case was eventually referred to the Inquisition, resulting in Galileo being summoned to trial in Rome. In 1633, Galileo arrived in Rome and was formally interrogated by the Inquistion. After confessing to having defended Copernican ideas in his "Dialogue", Galileo was sentenced to religious penances and was placed under house arrest in his villa in Arcetri for the remainder of his life.

During the next nine years, Galileo published "Mechanics" (a treatise on machines), "Letter to the Grand Duchess Christina", and "Discourse on Two New Sciences". He also continued in his efforts to promote the determination of longitude at sea using the moons of Jupiter as a reference point, a project he had been working on for much of his life. Although his idea was not considered practical for use on the high seas by either the Spanish or the Dutch, he was awarded a gold chain for his efforts from the Dutch States General, a reward which the Inquisition did not allow him to accept.

In addition to the numerous treatises and books that Galileo published during his lifetime, he was also the creator of several inventions. These include the hydrostatic balance (1586), a device for measuring the weight of objects in both air and water in order to determine their specific gravity; the one horse pump (1594), which raised 20 buckets of well water in continuous rotation; and the sector (1597), a proportional compass designed for gunnery and other uses.