Collections of these short tales with a moral were among the very first works--after the Bible--to be published on the printing press. It's amazing how many catch phrases come from these fables: Honesty is the best policy. Don't count your chickens before they've hatched. Look before you leap. Aesop himself, like Homer, may never have existed in history. Tradition makes him a slave in Asia Minor, possibly of Ethiopian descent, born in 620 and eventually freed for his cleverness becomes a counselor to kings and companion to philosophers. Herodotus, Aristophanes, Plato, Aristotle, Plutarch, Horace all mentioned Aesop and his tales, and the earliest surviving collection is from the first century. They're been used by orators and in primers ever since, and definitely should be read in the interest of cultural legacy. They're short. One of the most famous ones is only three lines:
Driven by hunger, a fox tried to reach some grapes hanging high on the vine but was unable to, although he leaped with all his strength. As he went away, the fox remarked, 'Oh, you aren't even ripe yet! I don't need any sour grapes.' People who speak disparagingly of things that they cannot attain would do well to apply this story to themselves.
To be honest, I tend to think these are best read by children, preferably in an illustrated edition. There's really no authoritative canon for the fables, the two primary collections from antiquity consist of only a few hundred tales. A lot of translations use antiquated language, or put the pithy tales into rather elaborated verse, or cut the moral, so you might want to scan various editions before deciding which to get. They're worth knowing, if only to be able to recognize where so many familiar stories and phrases come from.