Cover -- Contents -- Preface -- Alan Mathison Turing -- Chronology -- Preface to this volume -- Part I: Computability and Ordinal Logics -- Chapter 1. Historical Introduction (Solomon Feferman) -- Chapter 2. 1937 On Computable Numbers, with an Application to the Entscheidungsproblem -- Chapter 3. 1937 Computability and?-definability. 1937 The p-function in? -- K Conversion -- Chapter 4. 1938 Systems of Logic based on Ordinals -- Part II: Type Theory -- Chapter 5. General Introduction to Turing's work on Type Theory -- Published papers -- Chapter 6. 1942 (with M.H.A. Newman) A Formal Theorem in Church's Theory of Types -- Chapter 7. 1942 The Use of Dots as Brackets in Church's System -- Chapter 8. 1948 Practical Forms of Type Theory -- Unpublished papers -- Chapter 9. 1941 Some Theorems about Church's System -- Chapter 10. 1943-4 Practical Forms of Type Theory II -- Chapter 11. 1944-5 The Reform of Mathematical Notation -- Part III: Enigmas, Mysteries and Loose Ends -- Chapter 12. Turing's Treatise on the Enigma -- Chapter 13. Turing's Papers on Programming -- Chapter 14. Excerpt from: Programmer's Handbook for the Manchester Electronic Computer Mark II -- Chapter 15. Minimum Cost Sequential Analysis Excerpt from unpublished manuscript -- Chapter 16. The Nature of Turing and the Physical World (Andrew Hodges) -- Chapter 17. Letter from Robin Gandy to Max Newman -- Chapter 18. Royal Society Memoir -- Bibliography -- Lists of contents of other volumes -- Appendix: matters arising from other volumes -- Last Page.