The theory of motion developed by Galileo Galilei was a crucial step towards the modern, Newton's theory of motion. The important thing was Galileo's understanding of the motion as a state of body, as opposed to Aristotle's development or process of the actualisation of the form; Galileo's stress on the relativity of motion, the analysis of inertial motion, above all the mathematical description of the free fall and projectile trajectory served as a stepping stone for the analysis of the possibility of mathematical descriptions of all „terrestrial“ motions to the supporters of the „mechanical philosophy“ in the 17th century. Galileo's short curriculum vitae is presented in the thesis as an introduction to the context of those times, which is an important part for understanding the situation as a whole. Aristotle's theory, as the one accepted at the universities of Galilei time, together with its consequences upon cosmological research has been explored. The central part of the thesis describes Galilei's motivation for theoretical and empirical research of motion together with the results. The greatness of his theory lies in separating the cause of motion from the very description of the motion itself, and replacing the search for causes and principles of the world with a modern search of physical laws that describe it. By applying the abstract mathematical model to a real-life situation, Galileo experimentally proved that the actual body motion can really be mathematically described. Therewith he set the grounds for unity of practical experience and abstract science and opened the doors to experimental science and further development of physics. Galileo effectively changed the way people understood motion and introduced a different way of connecting motion and geometry. Also, the early reactions of the scientific community to Galilei motion theory are presented as well as the effect of this theory to the deveopment of physics. Finally, the controvertial topic of the relationship between religion and science is mentioned. The thesis contains a lesson plan presenting projectile motion, which is an obligatory part of four-year high school curriculum and a non-obligatory part of two and three-year high school curriculum.