Sir William Muir (April 27, 1819 - 1905), was a Scottish Orientalist.

He was born at Glasgow and educated at Kilmarnock Academy , at Glasgow and Edinburgh Universities, and at Haileybury College . In 1837 he entered the Bengal Civil Service. He served as secretary to the governor of the North-West Provinces, and as a member of the Agra revenue board, and during the Mutiny he was in charge of the intelligence department there. In 1865 he was made foreign secretary to the Indian Government. In 1867 he was knighted (K.C.S.I.), and in 1868 he became lieutenant-governor of the North-West Provinces. In 1874 he was appointed financial member of the Council, and retired in 1876, when he became a member of the Council of India in London. He had always taken an interest in educational matters, and it was chiefly through his exertions that the central college at Allahabad, known as Muir College, was built and endowed. Muir College later became a part of the Allahabad University. In 1885 he was elected principal of Edinburgh University in succession to Sir Alexander Grant, and held the post till 1903, when he retired.

Sir William Muir was a profound Arabic scholar, and made a careful study of the history of the time of Muhammad and the early caliphate. His chief books are a Life of Mahomet and History of Islam to the Era of the Hegira; Annals of the Early Caliphate; The Caliphate, an abridgment and continuation of the Annals, which brings the record down to the fall of the caliphate on the onset of the Mongols; The Koran: its Composition and Teaching; and The Mohammedan Controversy, a reprint of five essays published at intervals between 1885 and 1887. In 1888 he delivered the Rede lecture at Cambridge on The Early Caliphate and Rise of Islam.

He married in 1840 Elizabeth Huntly Wemyss (d. 1897), and had five sons and six daughters; four of his sons served in India, and one of them, Colonel A. N. Muir (d. 1899), was acting resident in Nepal.

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