A school is an assembly of teachers and a class is an assembly of students. In this sense, it has been existing for a long time. In the past, students sought teachers, found out them in far remote places, went to reside with them and learned things. Plato of ancient Greece was the one to first conceive and establish the idea of teachers and students coming to and meeting at a place and exchanging ideas in adherence to a pre-determined syllabus. He experimented with this novel idea in his Academy and therefore this system came to be known as the academic system of education. Plato was the founder of modern school system in a way. The last addition to the history of development of schools was the introduction of the Public School System by Thomas Arnold, the father of famous poet and critic Matthew Arnold.
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If you're not giving a specific school and asking who invented it, the answer would be in ancient Greece, where the first Universities began.