Little Red Riding Hood, as every schoolboy should know, but doesn't, was originally published by Charles Perrault - who, in point of fact, had much better style and flair than the anonymous writers who churn out the story in our modern children's books. But he didn't originate it. As a folk tale, many variations exist in Europe dating back hundreds of years. And it was bowdlerised even by the time he received it. Originally, it would have been a tale about an encounter with a werewolf.
This should be obvious once you think about it. When Little Red Riding Hood first met the wolf in the forest, how was he able to talk to her? Why wasn't she scared stiff? Why didn't he eat her up then and there? I always used to wonder about this when I was a boy.
Clearly, she met him in his natural, human form. Once she had told him her story, it set his evil mind at work. He repaired to somewhere private and performed whatever conjurations are necessary to transform into a wolf. (Montague Summers recorded such artifices as girding on an enchanted belt of wolf's fur, and then urinating around his clothes to turn them into a pile of stones until he returned.) As a wolf, he then ran all the way to Grandma's place, much faster than a human child could go, and polished off Grandma. Presumably, he then reverted to his human shape and, naked, crept into Grandma's bed, pulling the bedclothes up to his chin, and wrapping her bonnet tightly around his head as a disguise. When the unsuspecting grandchild said, "What a deep voice you have!" it was his masculine voice which nearly gave him away. When she said, "What big eyes ... big teeth etc you have!" he was busy turning into a wolf again.
It's pretty simple when you look at it.