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He studied Law at Sidney Sussex College, University of Cambridge (BA 1971), Harvard University (Joseph Hodges Choate Memorial Fellow, 1971–72; LLM 1972) and the University of Edinburgh School of Law (LLB 1974), and was admitted to the Faculty of Advocates in 1976, taking silk in 1988.
Born in Gosforth, Northumberland, he was educated at St Augustine's High School, Edinburgh and at the School of Law of the University of Edinburgh.
Brodie grew up in Alloa, Clackmannanshire and was educated at Dollar Academy in Clackmannanshire, and studied the School of Law of the University of Edinburgh (LL.B.) and the School of Law of the University of Virginia in the United States (LL.M.).