Original deposit: The papers provide extensive documentation of Adams's career in mathematics. There are Adams's lecture notes and other teaching material for courses at Manchester and Cambridge Universities, and material from conferences and seminars attended by Adams throughout the world, including drafts of Adams's contributions and notes of contributions by others. Although very few copies of Adams's own letters survive, correspondence from mathematical colleagues is a significant part of the papers. The correspondents include M.F. Atiyah, M.G. Barratt, P.J. Hilton, I.M. James and S. Mac Lane. Also of interest are the three Bedford School sixth form mathematics notebooks.

Supplementary deposit: the papers provide significant further documentation of Adams's research, lectures, including teaching material for courses at Cambridge, and publications. The correspondence is only a slight addition to the substantial original deposit and there is one biographical item: an intellectual 'family tree' compiled by Adams tracing pupils of J.H.C. Whitehead.