The Furies are just some of the monsters that hang out in the Underworld and that guard Hades, but they are a pretty deadly trio. They are sisters. One of the Furies poses as Percy's math teacher at Yancy Academy, Mrs. Dodds, and comes very close to killing him.
Mrs. Dodds was this little math teacher from Georgia who always wore a black leather jacket, even though she was fifty years old. She looked mean enough to ride a Harley right into your locker. She had come to Yancy halfway through the year, when our last math teacher had a nervous breakdown. (1.32)
The Furies chase Percy throughout his quest. Like all monsters, they are really good at smelling out demi-gods. They also have a knack for tormenting the dead.