It is generally accepted that Galileo was the first physicist to introduce the systematic use of mathematics into mechanics, although a mathematized statics and optics were already known by the Middle Ages. Furthermore, some historians of science, notably Koyre (for example in "Galileo and Plato", [9], pp. 150–179), consider this mathematization of physics to have been one of Galileo's greatest revolutionary contributions. Since this question has been relatively well discussed, what I would like to investigate in this paper is a related issue, the use of idealizationallaws by Galileo. I will try to show that Galileo was able to introduce mathematical laws into physics by making them idealizational. Furthermore, I think that by studying Galileo's use of idealization, we can understand better his revolutionary contributions — namely, what is it that differentiates in a radical way the kind of theory that he developed from the kind of theory that Aristotelian physics was and why experimentation came to be a fundamental tool for the development of classical physics.