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Galileo built telescopes over 30x magnification.
Galileo refused to believe the theory that the moon caused the tides, instead claiming it was caused by the Earth's rotation.
When Galileo discovered 4 of Jupiter's moons, he named them after the Grand Duke of Tuscany, Cosmo de Medici. After being named the Medicean stars, they later gained seperate names named after different people. They, as a whole, was later renamed the Galilean satellites in honor of Galileo himself.

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These are some quotes of Galileo. I am only going to describe how some of them refer to Galileo himself.

"You cannot teach a man anything; you can only help him find it within himself."
This probably refers to how Galileo refused Aristotelian physics and did most of his works off of Copernicanism, but people frowned upon said form of physics.

"All truths are easy to understand once they are discovered; the point is to discover them."
Galileo didn't have any way to prove any of the Copernican theories until he used the scientific method and some tools to discover that it was true.

If I were again beginning my studies, I would follow the advice of Plato and start with mathematics.
In the beginning of his career, his dad wanted him to have a career in medicine. But he still wanted to have a mathematical career , against protests of his father.

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(Scroll down, this is a long post)
In the January of 1610 he discovered 4 moons revolving around Jupiter. He also found the telescope could help you see way more stars than the naked eye. He wrote this because of financial problems, he didn't marry, but he did have an arrangement with a women to bear him children. He continued his studies on motion, and by 1609 he determined 2 things on motion that contradicted Aristotelian physics. But at this point, his career took a dramatic turn. He heard the telescope had been invented in the Netherlands, and figuring out the secret, he made an increasingly more powerful telescope. In August of that year he presented a 9-powered telescope to the Venetian Senate. He was rewarded with a doubling of his salary. He was now one of the highest paid professors in the university. He began observing space with instruments magnified up to 20 times in the fall, and in December he drew the phases of the moon as seen through the telescope, and he found that the surface of the moon is not smooth, as many people thought, but rough and uneven. In findings in a book, the Sidereal Messenger, and dedicated the book to the grand duke of Tuscany. He also named the moons after him and his family. He was rewarded with an appointment for mathematician and philosopher of the duke, and he returned to Tuscany in triumph. He was now a courtier and lived the life of a gentleman. Before he left Padua, he discovered the puzzling appearance of Saturn, caused by a ring surrounding it, and in Florence, he discovered that Venus goes through phases just like the moon., Though these discoveries did not prove that earth is not the center of the universe, they weakened Aristotelian cosmology. Paired with other discoveries of his, though, it did confirm his belief. His conversion to Copernicanism was a turning point in the scientific revolution. After a brief controversy about floating bodies, Galileo then focused on the heavens above. He entered a debate with Christoph Scheiner (a German member of the Society of Jesus and a professor of mathematics in Ingolstadt, Bavaria in Germany)about the nature of sunspots (you can find out about sunspots on the attached article) This controversy resulted in Galileo's "History and Demonstrations Concerning Sunspots and Their Properties" or "Letters on Sunspots", which was released in 1613. Against Scheiner, who, in an effort to save the perfection of the sun, claimed that sunspots are satellites of the sun, Galileo said sunspots are on or near the sun's surface. He supported his arguments with a bunch of detailed models of his observations. But then his Copercanism started to make trouble for him. In Pisa, he wrote a letter to one of his students the same year his argument on sunspots was released. The letter was about squaring the Copernican theory with certain biblical passages. Inaccurate copies of this letter were made by Galileo's enemies and sent to the inquisition in Rome. Galileo had to retrieve the inaccurate letters and send an accurate copy. Several Dominican fathers in Rome were complaining about Galileo in Rome, so he went to Rome to defend the Copernican cause. Before leaving, he finished an expanded version of the letter to his student, now addressed to the grand duke's mother and also his good friend. In this letter, he discussed the problem of interpreting biblical passages with regard to scientific discoveries but, except for one example, it did not interpret the bible. That had been reserved for approved theologians in the wake of the council of Trent,  and the beginning of the Catholic Counter-Reformation. But in Rome Copercanism was starting to get unpopular, and even though in 1615, when the cleric, Paolo Antonio Foscarini, published a book arguing that the Copernican theory did not conflict with scripture, Inquisition consultants examined the question and declared that the Copernican theory did, in fact, conflict with scripture. Foscarini's book was banned along with other technical and nontheological works. Copernicus' own book, "Six Books Concerning the Revolutions of the Heavenly Orbs" was suspended until corrected. Galileo was not mentioned directly in the decree, but he was admonished by Robert Cardinal Bellarmine (1542–1621) not to “hold or defend” the Copernican theory. An improperly prepared document made during this period says that Galileo was urged not to "hold, teach, or defend" the Copernican theory in any way possible, either orally, or in writing. Thus, Galileo was effectively muzzled on the Copernican issue. He only slowly recovered from this setback. Through a student, he entered a controversy (caused by the appearance of three comets)about the nature of comets. After several exchanges, mainly with Orazio Grassi (1583–1654), a professor of mathematics at the Collegio Romano, he finally entered the argument under his own name. The Assayer, published in 1623, was a brilliant polemic on physical reality and an exposition of the new scientific method. He also drew a distinction between the properties of external objects and the sensations they cause in us.
Galileo finished his book, Dialogue Concerning the Two Chief World Systems, Ptolemaic & Copernican),  in 1630.  Galileo’s approach to cosmology is fundamentally spatial and geometric: Earth’s axis retains its orientation in space as Earth circles the Sun, and bodies not under a force retain their velocity (although this inertia is ultimately circular). There was a strong reaction against the book and he was summoned by the Inquisition.  The case was at somewhat of an impasse, and, in what can only be called a plea bargain, Galileo confessed to having overstated his case. He was pronounced to be vehemently suspect of heresy and was condemned to life imprisonment and was made to abjure formally in 1634.  He died on January 8, 1642.

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Galileo was a well recognized mathematician, physicist, astronomer, and philosopher. Galileo supported the Copernican theory, which supports a sun-centered solar system.  He is an Italian scientist and scholar who made pioneering observations that laid the foundation for modern physics and astronomy. He also discovered 4 of Jupiter's moons.

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Article 1: Galileo (Britannica)

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In full:

Galileo Galilei

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Galileo (born February 15, 1564, Pisa [Italy]-died January 8, 1642, Arcetri, near Florence) Italian natural philosopher, astronomer, and mathematician who made fundamental contributions to the sciences of motion, astronomy, and strength of materials and to the development of the scientific method. His formulation of (circular) inertia, the law of falling bodies, and parabolic trajectories marked the beginning of a fundamental change in the study of motion. His insistence that the book of nature was written in the language of mathematics changed natural philosophy from a verbal, qualitative account to a mathematical one in which experimentation became a recognized method for discovering the facts of nature. Finally, his discoveries with the telescope revolutionized astronomy and paved the way for the acceptance of the Copernican heliocentric system, but his advocacy of that system eventually resulted in an Inquisition process against him.

Early life and career

Galileo was born in Pisa, Tuscany, on February 15, 1564, the oldest son of Vincenzo Galilei, a musician who made important contributions to the theory and practice of music and who may have performed some experiments with Galileo in 1588-89 on the relationship between pitch and the tension of strings. The family moved to Florence in the early 1570s, where the Galilei family had lived for generations. In his middle teens Galileo attended the monastery school at Vallombrosa, near Florence, and then in 1581 matriculated at the University of Pisa, where he was to study medicine. However, he became enamoured with mathematics and decided to make the mathematical subjects and philosophy his profession, against the protests of his father. Galileo then began to prepare himself to teach Aristotelian philosophy and mathematics, and several of his lectures have survived. In 1585 Galileo left the university without having obtained a degree, and for several years he gave private lessons in the mathematical subjects in Florence and Siena. During this period he designed a new form of hydrostatic balance for weighing small quantities and wrote a short treatise, La bilancetta ("The Little Balance"), that circulated in manuscript form. He also began his studies on motion, which he pursued steadily for the next two decades.

In 1588 Galileo applied for the chair of mathematics at the University of Bologna but was unsuccessful. His reputation was, however, increasing, and later that year he was asked to deliver two lectures to the Florentine Academy, a prestigious literary group, on the arrangement of the world in Dante's Inferno. He also found some ingenious theorems on centres of gravity (again, circulated in manuscript) that brought him recognition among mathematicians and the patronage of Guidobaldo del Monte (1545-1607), a nobleman and author of several important works on mechanics. As a result, he obtained the chair of mathematics at the University of Pisa in 1589. There, according to his first biographer, Vincenzo Viviani (1622-1703), Galileo demonstrated, by dropping bodies of different weights from the top of the famous Leaning Tower, that the speed of fall of a heavy object is not proportional to its weight, as Aristotle had claimed. The manuscript tract De motu ( On Motion), finished during this period, shows that Galileo was abandoning Aristotelian notions about motion and was instead taking an Archimedean approach to the problem. But his attacks on Aristotle made him unpopular with his colleagues, and in 1592 his contract was not renewed. His patrons, however, secured him the chair of mathematics at the University of Padua, where he taught from 1592 until 1610.

Although Galileo's salary was considerably higher there, his responsibilities as the head of the family (his father had died in 1591) meant that he was chronically pressed for money. His university salary could not cover all his expenses, and he therefore took in well-to-do boarding students whom he tutored privately in such subjects as fortification. He also sold a proportional compass, or sector, of his own devising, made by an artisan whom he employed in his house. Perhaps because of these financial problems, he did not marry, but he did have an arrangement with a Venetian woman, Marina Gamba, who bore him two daughters and a son. In the midst of his busy life he continued his research on motion, and by 1609 he had determined that the distance fallen by a body is proportional to the square of the elapsed time ( the law of falling bodies) and that the trajectory of a projectile is a parabola, both conclusions that contradicted Aristotelian physics.

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Galileo | Biography, Discoveries, Inventions, & Facts

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Galileo, the brilliant Italian polymath, revolutionized our understanding of the universe through his groundbreaking discoveries in astronomy and contributions to scientific methodology.

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Some time after that, he started to teach himself Aristotelian physics and mathematical subjects. He left the university without obtaining a degree. He then started to give private lessons on mathematical subjects in Florence and Sienna, both of which are in Tuscany, Italy. He designed a new form of hydrostatic balance for weighing small quantities and wrote a short treatise, "The Little Balance". He began studies on motion for 2 decades. During this period he applied for the chair of mathematics at the University of Bologna, in Emilia-Romagna, Italy but was unsuccessful. However, his reputation was increasing, and he was asked to give 2 lectures to the Florentine academy about the arrangement of the world in Dante's Inferno. He found ingenious theorems on the centers of gravity that brought him recognition among mathematicians and the patronage of Guidobaldo del Monte, a nobleman and the author of several works on mechanics. This, as a result, got him into the chair of mathematics at the University of Pisa. There, he proved that weight does not affect the rate at which something falls by dropping cannonballs of different weights off the infamous Leaning Tower of Pisa. His results shocked everyone. The manuscript tract written during this period, "In motion", shows he was abandoning Aristotelian physics and instead taking an Archimedean approach. But everyone was using Aristotelian physics at this time that it made him lose reputation and made him unpopular with his colleagues. His contract was not renewed in 1592. He then went to the University of Padua in Veneto, Italy. Although his salary was significantly higher there, his responsibility, (since his father died) as the head of the family, meant he was chronically pressed for money. His university salary could not cover all of his taxes and expenses, so he took in wealthy boarding students, whom he tutored privately in subjects such as fortification. He also sold a proportional compass, of his own creation. On the other hand, was made by an artisan whom he employed in his house.

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Galileo is born in Pisa, Tuscany on February 15, 1564. He moved to Florence (where his family had been living for generations) in the same region when he was 6 years old. He attended the monastery school at Vallombrosa, also in Tuscany, Italy. When he was in his college years, he went back to Pisa to go to the University of Pisa and studied medicine. He did experiments with his father, Vincenzo Galilei, a lutanist, on the relationship between pitch and tension of strings. He became enamored with mathematics, so he made mathematical subjects and philosophy his career against his father, who wanted him to have a career in medicine.