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This class contains virtually no extended exchanges of correspondence, as the great majority of letters are incoming, with very few carbons of Adams's replies. The content is essentially mathematical; chiefly requests for Adams's advice or comments on specific problems, reflecting Adams's high standing in his field. Of special interest is the extensive correspondence from M. F. Atiyah, M. G. Barratt, P. J. Hilton, I. M. James, A. Liulevičius, S. Mac Lane, and C. W. Wilkerson.

Where applicable reference has been made to Adams's List of Publications (A.2)

Items C. 1 - C.344 consist of lectures etc as part of Adams' role in teaching, These are further subdivided according to subject:
C1-C89 Algebra
C90-C129 Geometry
C130-C143 Homology
C144-C218 Homotopy
C219-C230 K-theory
C241-C248 Lie Groups
C249-C263 Representation Theory
C264-C315 Topology
C316-C344 Miscellaneous

C.345 - C.646 are from conferences and seminars he attended and C.647 - C.708 consist of lectures by others.

The material is principally Adams's undated MS drafts, notes and calculations documenting his research from the 1950s until his death. It was found in Adams's own folders with titles inscribed thereon. These titles have been reproduced in the catalogue entries and form the basis for the arrangement of the material in an alphabetical sequence. At the end of this sequence is miscellaneous research material including 'work done' and 'work in progress'. The contents of bulky folders have been subdivided for ease of reference.

The collection is particularly noteworthy for its coverage of Adams's lectures, research and incoming correspondence.
Section A, Biographical, is not substantial. It includes a little material of Adams's relating to his own career including three Bedford School notebooks and his PhD thesis, and material assembled by I M James during the preparation of his Royal Society memoir.
Section B, Research, provides extensive documentation of Adams's research from the 1950s until his death. It is presented in an alphabetical sequence arranged by subject title.
Section C, Lectures, is the largest in the collection. Two subsections comprise Adams's lecture notes and other teaching material for courses given at Manchester and Cambridge, and material from conferences and seminars attended by Adams throughout the world including drafts of Adams's contributions and notes of contributions by others. A third subsection consists of Adams's ms notes found in filing cabinet drawers labelled 'Other people's lectures'. It includes notes taken by Adams as an undergraduate at Cambridge in 1949.
Section D, Publications, is very slight. It includes drafts of a few of Adams's scientific papers.
Section E, Correspondence, contains virtually no extended exchanges of correspondence as very few copies of Adams's own letters survive. There is, however, significant correspondence from colleagues such as M F (later Sir Michael) Atiyah, M G Barratt, P J Hilton, I M James and S MacLane, sometimes extending over a period of twenty or thirty years.

This section contains material gathered after Adams's death, primarily by I. M. James while working on the memoir for the Royal Society published in 1990. This includes letters from former colleagues and students with descriptions and stories about Adams, and includes a photograph taken of Adams after climbing on top of a sculpture at midnight and the eulogy delivered in Trinity College Chapel by J. P. May at the memorial service in April 1993.

Lecture notes for course of eight summer-term lectures. Some sheets marked 'OLD'.

Some material on back of duplicated typescript sheets 1954. At B.100 is rough draft of letter to G W Whitehead.

The correspondence chiefly relates to work towards two 1988 joint publications by Adams, Jackowski, J-P Haeberly and J P May 'A generalisation of the Segal conjecture' (Bibliog.no.78) and 'A generalisation of the Atiyah-Segal completion theorem'

Questionnaires on Adams's geometry lectures completed by students 1982; letter from student requesting 'a lecture on lie groups' 25 April 1985, with ms notes on lie groups.

The correspondence chiefly relates to work towards two 1988 joint publications by Adams, Jackowski, J-P Haeberly and J P May 'A generalisation of the Segal conjecture' (Bibliog.no.78) and 'A generalisation of the Atiyah-Segal completion theorem'

'Geometry hand-outs'.

.

Notes on work of J P May.

'Some applications of K-theory to homotopy theory', ms notes and tables.

Lecture notes.

'Killing htpy groups: stable case'.

'Killing htpy groups: unstable case'.

Questionnaires on content and style of Adams's IB geometry lectures completed by students 1974.

'Calculations using method of "killing htpy groups"...'.

'IB Geometry' example sheets; correspondence from D W Babbage re geometry examination questions 1974-75.