Mathematics of Magic Squares

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I have seen many popular accounts of simple magic squares but I would like to find a proper mathematical background to understanding magic squares. What background knowledge do I need. I am a retired senior school maths teacher.

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There is a 150 year old book by Symes on Magic Squares. Modern books will take a more abstract approach which may get in the way of learning the classical subject of magic squares. I'm assuming you don't want to get side-tracked with excessive linear algebra.