when was it published?
The Fellowship of the Ring - 29 July 1954, The Two Towers - 11 November 1954 and The Return of the King - 20 October 1955 in the United Kingdom.
The Lord of the Rings
For publication, the work was divided into three volumes to minimize any potential financial loss due to the high cost of type-setting and modest anticipated sales: "The Fellowship of the Ring" (Books I and II), "The Two Towers" (Books III and IV), and "The Return of the King" (Books V and VI plus six appendices). Delays in producing appendices, maps and especially an index led to the volumes being published later than originally hoped – on 29 July 1954, on 11 November 1954 and on 20 October 1955 respectively in the United Kingdom. 
where did tolkien write lord of the rings 20 Northmoor Road in North Oxford. what genre does it come under? High fantasy works.
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The Lord of the Rings [SEP] Publication history
For publication, the work was divided into three volumes to minimize any potential financial loss due to the high cost of type-setting and modest anticipated sales: "The Fellowship of the Ring" (Books I and II), "The Two Towers" (Books III and IV), and "The Return of the King" (Books V and VI plus six appendices). Delays in producing appendices, maps and especially an index led to the volumes being published later than originally hoped – on 29 July 1954, on 11 November 1954 and on 20 October 1955 respectively in the United Kingdom. In the United States, Houghton Mifflin published "The Fellowship of the Ring" on 21 October 1954, "The Two Towers" on 21 April 1955, and "The Return of the King" on 5 January 1956.