Galileo tended to refer to himself only by his given name. At the time, surnames were optional in Italy, and his given name had the same origin as his sometimes-family name, Galilei. Both his given and family name ultimately derive from an ancestor, Galileo Bonaiuti, an important physician, professor, and politician in Florence in the 15th century; his descendants had come to refer to themselves as Galilei in his honor in the late 14th century.

Galileo was born in Pisa (then part of the Duchy of Florence), Italy, on 15 February 1564, the first of six children of Vincenzo Galilei, a lutenist, composer, and music theorist, and Giulia (née Ammannati), who had married in 1562.

Galileo became an accomplished lutenist himself and would have learned early from his father a scepticism for established authority, the value of well-measured or quantified experimentation, an appreciation for a periodic or musical measure of time or rhythm, as well as the results expected from a combination of mathematics and experiment.

When Galileo Galilei was eight, his family moved to Florence, but he was left with Jacopo Borghini for two years.

Galileo was educated from 1575 to 1578 in the Vallombrosa Abbey, about 30 km southeast of Florence.

Although Galileo seriously considered the priesthood as a young man, at his father's urging he instead enrolled in 1580 at the University of Pisa for a medical degree.

In 1581, when Galileo was studying medicine, he noticed a swinging chandelier, which air currents shifted about to swing in larger and smaller arcs. To him, it seemed, by comparison with his heartbeat, that the chandelier took the same amount of time to swing back and forth, no matter how far it was swinging. When he returned home, he set up two pendulums of equal length and swung one with a large sweep and the other with a small sweep and found that they kept time together. It was not until the work of Christiaan Huygens, almost one hundred years later, that the tautochrone nature of a swinging pendulum was used to create an accurate timepiece.

In the Catholic world prior to Galileo's conflict with the Church, the majority of educated people subscribed to the Aristotelian geocentric view that the Earth was the center of the universe and that all heavenly bodies revolved around the Earth, though Copernican theories were used to reform the calendar in 1582.

When he did refer to himself with more than one name, it was sometimes as Galileo Galilei Linceo, a reference to his being a member of the Academy of Lincei, an elite pro-science organization in Italy. It was common for mid-sixteenth-century Tuscan families to name the eldest son after the parents' surname.

Galileo created a thermoscope, a forerunner of the thermometer, and, in 1586, published a small book on the design of a hydrostatic balance he had invented (which first brought him to the attention of the scholarly world).

Galileo also studied disegno, a term encompassing fine art, and, in 1588, obtained the position of instructor in the Accademia delle Arti del Disegno in Florence, teaching perspective and chiaroscuro.

In 1589, Galileo was appointed to the chair of mathematics in Pisa.

In 1591, his father died, and Galileo was entrusted with the care of his younger brother Michelagnolo.

In 1592, Galileo moved to the University of Padua where he taught geometry, mechanics, and astronomy until 1610.

In 1593, Galileo constructed a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

Galileo made a number of contributions to what is now known as engineering, as distinct from pure physics. Between 1595 and 1598, Galileo devised and improved a geometric and military compass suitable for use by gunners and surveyors.

Despite being a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba. They had two daughters, Virginia (born 1600) and Livia (born 1601), and a son, Vincenzo (born 1606).

Tycho and others had observed the supernova of 1572. Ottavio Brenzoni's letter of 15 January 1605 to Galileo brought the 1572 supernova and the less bright nova of 1601 to Galileo's notice. Galileo observed and discussed Kepler's supernova in 1604. Since these new stars displayed no detectable diurnal parallax, Galileo concluded that they were distant stars, and, therefore, disproved the Aristotelian belief in the immutability of the heavens.

Based only on uncertain descriptions of the first practical telescope which Hans Lippershey tried to patent in the Netherlands in 1608, Galileo, in the following year, made a telescope with about 3x magnification. He later made improved versions with up to about 30x magnification.

In 1609, Galileo 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, at a banquet held in 1611 by Prince Federico Cesi to make Galileo a member of his Accademia dei Lincei.

On November 30, 1609 Galileo aimed his telescope at the Moon. While not being the first person to observe the Moon through a telescope (English mathematician Thomas Harriot had done it four months before but only saw a "strange spottednesse"), Galileo was the first to deduce the cause of the uneven waning as light occlusion from lunar mountains and craters. In his study, he also made topographical charts, estimating the heights of the mountains. The Moon was not what was long thought to have been a translucent and perfect sphere, as Aristotle claimed, and hardly the first "planet", an "eternal pearl to magnificently ascend into the heavenly empyrian", as put forth by Dante. Galileo is sometimes credited with the discovery of the lunar libration in latitude in 1632, although Thomas Harriot or William Gilbert might have done it before.

On 7 January 1610, Galileo observed with his telescope what he described at the time as "three fixed stars, totally invisible by their smallness", all close to Jupiter, and lying on a straight line through it.

Galileo began his telescopic observations in the later part of 1609, and by March 1610 was able to publish a small book, The Starry Messenger (Sidereus Nuncius), describing some of his discoveries: mountains on the Moon, lesser moons in orbit around Jupiter, and the resolution of what had been thought to be very cloudy masses in the sky (nebulae) into collections of stars too faint to see individually without a telescope. Other observations followed, including the phases of Venus and the existence of sunspots.

Galileo's contributions caused difficulties for theologians and natural philosophers of the time, as they contradicted scientific and philosophical ideas based on those of Aristotle and Ptolemy and closely associated with the Catholic Church. In particular, Galileo's observations of the phases of Venus, which showed it to circle the Sun, and the observation of moons orbiting Jupiter, contradicted the geocentric model of Ptolemy, which was backed and accepted by the Roman Catholic Church, and supported the Copernican model advanced by Galileo.

In 1610, Galileo used a telescope at close range to magnify the parts of insects.

In a letter to Kepler of August 1610, Galileo complained that some of the philosophers who opposed his discoveries had refused even to look through a telescope: My dear Kepler, I wish that we might laugh at the remarkable stupidity of the common herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.

From September 1610, Galileo observed that Venus exhibited a full set of phases similar to that of the Moon. The heliocentric model of the Solar System developed by Nicolaus Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun.

In 1611, Galileo visited the Collegium Romanum in Rome, where the Jesuit astronomers by that time had repeated his observations. Christoph Grienberger, one of the Jesuit scholars on the faculty, sympathized with Galileo's theories, but was asked to defend the Aristotelian viewpoint by Claudio Acquaviva, the Father General of the Jesuits. Not all of Galileo's claims were completely accepted: Christopher Clavius, the most distinguished astronomer of his age, never was reconciled to the idea of mountains on the Moon, and outside the collegium many still disputed the reality of the observations.

One of the first suggestions of heresy that Galileo had to deal with came in 1613 from a professor of philosophy, poet and specialist in Greek literature, Cosimo Boscaglia. In conversation with Galileo's patron Cosimo II de' Medici and Cosimo's mother Christina of Lorraine, Boscaglia said that the telescopic discoveries were valid, but that the motion of the Earth was obviously contrary to Scripture: Dr. Boscaglia had talked to Madame [Christina] for a while, and though he conceded all the things you have discovered in the sky, he said that the motion of the Earth was incredible and could not be, particularly since Holy Scripture obviously was contrary to such motion.

Tommaso Caccini, a Dominican friar, appears to have made the first dangerous attack on Galileo. Preaching a sermon in Florence at the end of 1614, he denounced Galileo, his associates, and mathematicians in general (a category that included astronomers).

In late 1614 or early 1615, one of Caccini's fellow Dominicans, Niccolò Lorini, acquired a copy of Galileo's letter to Castelli. Lorini and other Dominicans at the Convent of San Marco considered the letter of doubtful orthodoxy, in part because it may have violated the decrees of the Council of Trent: check unbridled spirits, [the Holy Council] decrees that no one relying on his own judgement shall, in matters of faith and morals pertaining to the edification of Christian doctrine, distorting the Scriptures in accordance with his own conceptions, presume to interpret them contrary to that sense which the holy mother Church... has held or holds... — Decree of the Council of Trent (1545–1563). Quoted in Langford, 1992.

Lorini and his colleagues decided to bring Galileo's letter to the attention of the Inquisition. In February 1615 Lorini accordingly sent a copy to the Secretary of the Inquisition, Cardinal Paolo Emilio Sfondrati, with a covering letter critical of Galileo's supporters: All our Fathers of the devout Convent of St. Mark feel that the letter contains many statements which seem presumptuous or suspect, as when it states that the words of Holy Scripture do not mean what they say; that in discussions about natural phenomena the authority of Scripture should rank last... . [The followers of Galileo] were taking it upon themselves to expound the Holy Scripture according to their private lights and in a manner different from the common interpretation of the Fathers of the Church... — Letter from Lorini to Cardinal Sfrondato, Inquisitor in Rome, 1615. Quoted in Langford, 1992.

On March 19, Caccini arrived at the Inquisition's offices in Rome to denounce Galileo for his Copernicanism and various other alleged heresies supposedly being spread by his pupils.

Cardinal Robert Bellarmine, one of the most respected Catholic theologians of the time, was called on to adjudicate the dispute between Galileo and his opponents. The question of heliocentrism had first been raised with Cardinal Bellarmine, in the case of Paolo Antonio Foscarini, a Carmelite father; Foscarini had published a book, Lettera ... sopra l'opinione ... del Copernico, which attempted to reconcile Copernicus with the biblical passages that seemed to be in contradiction. Bellarmine at first expressed the opinion that Copernicus's book would not be banned, but would at most require some editing so as to present the theory purely as a calculating device for "saving the appearances" (i.e. preserving the observable evidence). Foscarini sent a copy of his book to Bellarmine, who replied in a letter of April 12, 1615.

Cardinal Bellarmine had written in 1615 that the Copernican system could not be defended without "a true physical demonstration that the sun does not circle the earth but the earth circles the sun".

Galileo was defended on the spot by his former student Benedetto Castelli, now a professor of mathematics and Benedictine abbot. The exchange having been reported to Galileo by Castelli, Galileo decided to write a letter to Castelli, expounding his views on what he considered the most appropriate way of treating scriptural passages which made assertions about natural phenomena. Later, in 1615, he expanded this into his much longer Letter to the Grand Duchess Christina.

Galileo soon heard reports that Lorini had obtained a copy of his letter to Castelli and was claiming that it contained many heresies. He also heard that Caccini had gone to Rome and suspected him of trying to stir up trouble with Lorini's copy of the letter. As 1615 wore on he became more concerned, and eventually determined to go to Rome as soon as his health permitted, which it did at the end of the year. By presenting his case there, he hoped to clear his name of any suspicion of heresy, and to persuade the Church authorities not to suppress heliocentric ideas.

In addition to Bellarmine, Monsignor Francesco Ingoli initiated a debate with Galileo, sending him in January 1616 an essay disputing the Copernican system. Galileo later stated that he believed this essay to have been instrumental in the action against Copernicanism that followed in February.

On February 19, 1616, the Inquisition asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe. Historians of the Galileo affair have offered different accounts of why the matter was referred to the qualifiers at this time. Beretta points out that the Inquisition had taken a deposition from Gianozzi Attavanti in November 1615, as part of its investigation into the denunciations of Galileo by Lorini and Caccini.

On February 24 the Qualifiers delivered their unanimous report: the proposition that the Sun is stationary at the centre of the universe is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture"; the proposition that the Earth moves and is not at the centre of the universe "receives the same judgement in philosophy; and ... in regard to theological truth it is at least erroneous in faith."

At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence and ordered, to abstain completely from teaching or defending this doctrine and opinion or from discussing it... to abandon completely... the opinion that the sun stands still at the center of the world and the earth moves, and henceforth not to hold, teach, or defend it in any way whatever, either orally or in writing. — The Inquisition's injunction against Galileo, 1616.

For Galileo, the tides were caused by the sloshing back and forth of water in the seas as a point on the Earth's surface sped up and slowed down because of the Earth's rotation on its axis and revolution around the Sun. He circulated his first account of the tides in 1616, addressed to Cardinal Orsini.

Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude of stars packed so densely that they appeared from Earth to be clouds. He located many other stars too distant to be visible with the naked eye. He observed the double star Mizar in Ursa Major in 1617.

Because The Assayer contains such a wealth of Galileo's ideas on how science should be practised, it has been referred to as his scientific manifesto. Early in 1619, Father Grassi had anonymously published a pamphlet, An Astronomical Disputation on the Three Comets of the Year 1618, which discussed the nature of a comet that had appeared late in November of the previous year. Grassi concluded that the comet was a fiery body which had moved along a segment of a great circle at a constant distance from the earth, and since it moved in the sky more slowly than the Moon, it must be farther away than the Moon.

In 1619, Galileo became embroiled in a controversy with Father Orazio Grassi, professor of mathematics at the Jesuit Collegio Romano. It began as a dispute over the nature of comets, but by the time Galileo had published The Assayer (Il Saggiatore) in 1623, his last salvo in the dispute, it had become a much wider controversy over the very nature of science itself.

Grassi's arguments and conclusions were criticized in a subsequent article, Discourse on Comets, published under the name of one of Galileo's disciples, a Florentine lawyer named Mario Guiducci, although it had been largely written by Galileo himself.

In 1623, Pope Gregory XV died and was succeeded by Pope Urban VIII who showed greater favor to Galileo, particularly after Galileo traveled to Rome to congratulate the new Pontiff.

By 1624, Galileo had used a compound microscope. He gave one of these instruments to Cardinal Zollern in May of that year for presentation to the Duke of Bavaria, and in September, he sent another to Prince Cesi.

Galileo's Dialogue Concerning the Two Chief World Systems, which was published in 1632 to great popularity. Was an account of conversations between a Copernican scientist, Salviati, an impartial and witty scholar named Sagredo, and a ponderous Aristotelian named Simplicio, who employed stock arguments in support of geocentricity, and was depicted in the book as being an intellectually inept fool.

With the loss of many of his defenders in Rome because of Dialogue Concerning the Two Chief World Systems, in 1633 Galileo was ordered to stand trial on suspicion of heresy "for holding as true the false doctrine taught by some that the sun is the center of the world" against the 1616 condemnation, since "it was decided at the Holy Congregation [...] on 25 Feb 1616 that [...] the Holy Office would give you an injunction to abandon this doctrine, not to teach it to others, not to defend it, and not to treat of it; and that if you did not acquiesce in this injunction, you should be imprisoned".

Galileo was found guilty, and the sentence of the Inquisition, issued on 22 June 1633, was in three essential parts: Galileo was found "vehemently suspect of heresy", namely of having held the opinions that the Sun lies motionless at the center of the universe, that the Earth is not at its centre and moves, and that one may hold and defend an opinion as probable after it has been declared contrary to Holy Scripture. He was required to "abjure, curse, and detest" those opinions. He was sentenced to formal imprisonment at the pleasure of the Inquisition. On the following day this was commuted to house arrest, which he remained under for the rest of his life. His offending Dialogue was banned; and in an action not announced at the trial, publication of any of his works was forbidden, including any he might write in the future.

In 1638, Galileo described an experimental method to measure the speed of light by arranging that two observers, each having lanterns equipped with shutters, observe each other's lanterns at some distance. The first observer opens the shutter of his lamp, and, the second, upon seeing the light, immediately opens the shutter of his own lantern. The time between the first observer's opening his shutter and seeing the light from the second observer's lamp indicates the time it takes light to travel back and forth between the two observers. Galileo reported that when he tried this at a distance of less than a mile, he was unable to determine whether or not the light appeared instantaneously.

After a period with the friendly Archbishop Piccolomini in Siena, Galileo was allowed to return to his villa at Arcetri near Florence, where he spent the rest of his life under house arrest. He continued his work on mechanics, and in 1638 he published a scientific book in Holland. His standing would remain questioned at every turn. In March 1641, Vincentio Reinieri, a follower and pupil of Galileo, wrote him at Arcetri that an Inquisitor had recently compelled the author of a book printed at Florence to change the words "most distinguished Galileo" to "Galileo, man of noted name".

Galileo continued to receive visitors until 1642, when, after suffering fever and heart palpitations, he died on 8 January 1642, aged 77. The Grand Duke of Tuscany, Ferdinando II, wished to bury him in the main body of the Basilica of Santa Croce, next to the tombs of his father and other ancestors, and to erect a marble mausoleum in his honor.

The Galileo affair was largely forgotten after Galileo's death, and the controversy subsided. The Inquisition's ban on reprinting Galileo's works was lifted in 1718 when permission was granted to publish an edition of his works (excluding the condemned Dialogue) in Florence.

In 1741, Pope Benedict XIV authorized the publication of an edition of Galileo's complete scientific works which included a mildly censored version of the Dialogue.

On 15 February 1990, in a speech delivered at the Sapienza University of Rome, Cardinal Ratzinger (later Pope Benedict XVI) cited some current views on the Galileo affair as forming what he called "a symptomatic case that permits us to see how deep the self-doubt of the modern age, of science and technology goes today".

On 31 October 1992, Pope John Paul II expressed regret for how the Galileo affair was handled, and issued a declaration acknowledging the errors committed by the Catholic Church tribunal that judged the scientific positions of Galileo Galilei, as the result of a study conducted by the Pontifical Council for Culture.

In March 2008, the head of the Pontifical Academy of Sciences, Nicola Cabibbo, announced a plan to honor Galileo by erecting a statue of him inside the Vatican walls.

In December of the same year, during events to mark the 400th anniversary of Galileo's earliest telescopic observations, Pope Benedict XVI praised his contributions to astronomy.

A month later, however, the head of the Pontifical Council for Culture, Gianfranco Ravasi, revealed that the plan to erect a statue of Galileo on the grounds of the Vatican had been suspended.