Newton reached the main results that would later constitute his theory of fluxions between the end of 1663 and the Fall of 1666. Many notes dating back to this period have been conserved, and D. T. Whiteside has published them in the first volume of Newton's Mathematical Papers. They can be used to reconstruct the evolution of Newton's ideas at the very beginning of his mathematical researches and his progressive achievements. The present paper present such a reconstruction.