Johannes Kepler was the assistant of the Danish astronomer Tycho Brahe who spent several years making accurate measurements of the position of stars and planets. Kepler was a good mathematician and studied Tycho’s data with great attention. This chapter introduces immediately the principle of least action and show that Newton’s laws are a consequence of it. Kepler was a mathematician and astronomer who carefully studied the motion of the Moon and the planets known at the time. At the time of Kepler, the regularity of the motion of stars and planets was assumed to be a reflection of the perfection of the Creator. The chapter argues that if a dynamical system is invariant under rotations and time translations, then it conserves, respectively, angular momentum and energy. Newton’s law of gravitation has been introduced without a good discussion because we were interested mostly in the mathematical structure.