Pedagogy is the art or science of being a teacher and of learning. The word pedagogy comes from the Greek word paidagōgeō, which means "to lead the child."  In Ancient Greece, rich men had a slave to instruct their sons as a tutor, or to take them to the academy. Girls were almost entirely home schooled but many boys went to school even if they had a tutor.
An academic degree is sometimes given for pedagogy. In the United States of America and Great Britain, you can earn a degree in education at the Bachelor's (undergraduate; BA or BS) or Master's (graduate; MA or MS) level. You can also earn an advanced degree called either a Doctor of Education (Ed.D.), or a Doctor of Philosophy (Ph.D.); you can also get a degree for specific things, like a Doctor of Music degree in piano pedagogy.
Some people do not like the idea of pedagogy. They say that learning is something that a person does for themselves, not something that a person imposes on a person. Pedagogy is mainly credited and acknowledged in Western society, but not regarded as a good thing in some Eastern secular and fundamentalist societies.