The story of "Little Red Riding Hood" was first published by French author Charles Perrault, who was influenced by previous oral tellings of the tale. This version, of course, later proved to be of tremendous influence to Jacob and Wilhelm Grimm (or the Brothers Grimm) in their own rendition of the story. Since you are probably most familiar with the Grimm's version, let's summarize that one in seventy words, as you have requested:

Little Red Riding Hood is sent to deliver goodies to her sick grandmother. On the way, Little Red meet the Wolf, who convinces her to stray from the path to pick flowers. The Wolf hurries to the house and eats the grandmother. When Little Red arrives, the Wolf pretends to be her grandmother and eats the girl as well. A huntsman saves the pair by cutting open the Wolf's belly.