While in the University, Galileo did extensive experimentation with pendulums, finding that they nearly return to the height at which they were released, that different pendulums have different periods (independent of bob weight and amplitude), and that the square of the period varies directly with the pendulum's length (and it does not not depend on the arc of the swing). He later used pendulums to make a clock (1641). Galileo also found that the speed at which bodies fall does not depend on their weight. He documented these discoveries in his book called, "De Motu" (meaning "On Motion").

Galileo was appointed professor of mathematics at the University of Padua (1592-1610). In 1593, Galileo invented the thermometer. Some of his many other inventions included a revolutionary water pump and a hydrostatic balance (a device that weighed things accurately in either air or water).

In 1609, Galileo was the first person to use a telescope to observe the skies (after hearing about Hans Lippershey's newly-invented telescope). Galileo discovered the rings of Saturn (1610), was the first person to see the four major moons of Jupiter (1610), observed the phases of Venus, studied sunspots, and discovered many other important phenomena.

In 1610, Galileo moved to Florence, Italy, where he pursued his research at the University of Florence and the Court of the Medici family, then headed by Cosimo II, the Grand Duke of Tuscany.

After discussing and publishing the many discoveries he made using his telescope, including the confirmation that the Earth orbits the Sun (this is called the Copernican system), Galileo was charged with heresy by the Inquisition. The Inquisition was an institution run by the Catholic church for the eradication of heresies and heretics (ideas and people that ran counter to teaching of the church). The church preferred a geocentric model of the universe (a model in which the Earth is at the center of the universe) to Galileo's heliocentric model of the Solar System (in which the Sun is at the center of the Solar System, and the Earth and other planets orbit around the Sun). After being warned not to discuss or publish his heretical theory, Galileo disobeyed and published his book, "Dialogue Concerning the Two Chief World Systems." He was found guilty of heresy in 1633 and was put under house arrest for life. He died in 1642, at his home near Florence, Italy.