I will give a leisurely overview of the themes mentioned in the title, which were born from astronomy (celestial mechanics) together with modern science itself. I will try to emphasize both some important well-known and less well-known physical phenomena and some mathematical techniques (normal forms, small divisors, KAM techniques etc.) which in large part evolved from the groundbreaking work of H.Poincar\'e and constitute the contemporary framework of this still very active domain.