After graduation, Maxwell taught
Classics at
Madras College in St Andrews before being appointed as an archaeological investigator at the
Royal Commission on the Ancient and Historical Monuments of Scotland (RCAHMS) in 1964. At RCAHMS, Maxwell contributed to all seven volumes of the Survey of Argyll as well as a volume on the Prehistoric and Roman Monuments of Lanarkshire. He also edited two landscape survey volumes on Perthshire. Maxwell established the aerial survey programme at RCAHMS from 1976. In this work, he was able to make a number of significant discoveries of new sites from the air, some of which he subsequently excavated, including the Roman fort of Doune in Stirlingshire. He discovered over a dozen Roman forts and fortlets, leading to a cartoon in The Times. Maxwell's primary research interests concerned the Roman army in Scotland, about which he published numerous papers in journals including the Proceedings of the
Society of Antiquaries of Scotland, Glasgow Archaeological Journal and Britannia. He co-authored the standard text on the Antonine Wall as well as an overview of the Romans in Scotland and a volume on the search for the
Battle of Mons Graupius. He was on the organising committee for the 12th International
Congress of Roman Frontier Studies which took place in Stirling in 1979. Maxwell was editor of the Proceedings of the
Society of Antiquaries of Scotland from 1965–69 and was elected President of the Society from 1993-1996. He was elected as a Fellow of the
Royal Society of Edinburgh in 1998 and was appointed an Honorary Professor at the
University of St Andrews. and once featured on BBC Scotland's
The Beechgrove Garden. Maxwell died in Fife on 19 November 2024. == Selected publications ==