What is the name of the ancient greek who wrote a group of fables greek man who wrote a group of fables?

You probably mean Aesop, a Greek fabulist that wrote what is collectively known as "Aesop's Fables."

Although we have no writings by him, his stories are found in a variety of sources from different time periods. Some details of his life can also be found in sources like Aristotle, Herodotus and Plutarch.