Having been educated as a member of the Society of Friends and taken the degree of B.A. at London University, he became a partner in the banking house of Hodgkin, Barnett & Co., Newcastle-on-Tyne, a firm afterwards amalgamated with Lloyds Bank.

While continuing in business as a banker, Hodgkin devoted a good deal of time to historical study, and soon became a leading authority on the history of the early middle ages, his books being indispensable to all students of this period. His chief works are:

• Italy and her Invaders (8 vols., Oxford, 1880-1899)
• The Dynasty of Theodosius (Oxford, 1889)
• Theodoric the Goth (London, 1891)
• an introduction to the Letters of Cassiodorus (London, 1886).

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