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This article surveys all known fields of network coding theory and leads the reader through the antecedents of the network coding theory to the most recent results, considering also information theory and matroid theory. By focusing on providing ideas and not formulas, this survey is both fitted for the taste of readers who are mathematically oriented and newcomers to the area. Additionally, this survey also includes an innovative and clear graph representation of the most prominent literature on network coding theory, its relevance and evolution from the very beginning till today.