Mankind invented school. Ever since the beginning of time older creatures have been teaching their children. I say creatures because animals do it too. If you are referring to organized education and are wanting a singular name, I doubt you will find one. I dont even think you will be able to place it on a single group of people...(i.e. Romans, Egyptians, etc). Learning from others is just a basic, needed form of communication. Organized teaching just made it easier.
Confucius is believed to have been the first to open a public school in the 6th century in China. However schools have existed for the elites of societies in all cultures since writing and the alphabet were created.