TITLE: Arnold diffusion: an overview through Dynamical Astronomy AUTHOR: Pablo M. Cincotta Facultat de Ciencias Astronomicas y Geofisicas, Universidad Nacional de La Plata, Paseo del Bosque, 1900 La Plata, Argentina. ABSTRACT: The aim of this work is to review the fundamental ideas behind the stability problem, emphasizing the differences between two well-known mechanisms that could lead to chaos, namely overlap of resonances and Arnold diffusion. Here we restrict the discussion to multidimensional autonomous Hamiltonian systems which are of major relevance in Dynamical Astronomy. Arnold diffusion is reviewed in a standard mathematical language, by means of different tools such as heuristic reasoning, graphic and geometrical considerations and numerical experiments. In this direction the pioneer work due to Chiriko(1979) is followed, but including additional notes, further examples and useful discussions that may well illuminate the understanding of Arnold diffusion.We also summarize the main difficulties when coping with this instability, from both the analytical and numerical sides of the problem. The discussion whether Arnold diffusion could play any role in the dynamical evolution of, for instance elliptical galaxies, is also included.