The Hénon-Heiles system was originally proposed to describe the dynamical behavior of galaxies, but this system has been widely applied in dynamical systems as it displays many details in phase space. This work presents the formalism to describe the Hénon-Heiles system and a qualitative approach to the dynamical behavior. The growth of the chaotic region in phase space is observed by Poincaré Surface Sections, as the total energy increases. Islands of regularity remain around stable points and there are relevant sticky phenomena.