CONTENTS PART I Introduction............................................................................................... 3 1. General solution.................................................................................. 4 2. Preliminaries and notation................................................................ 5 3. $C^p$ solutions in $\mathfrak{C}$*................................................ 7 4. Change of variables........................................................................... 13 5. Continuous solutions in $\mathfrak{C}$....................................... 15 6. $C^p$ solutions in a neighbourhood of the origin....................... 18 7. Final comments.................................................................................. 26 PART II 8. Introductory remarks.......................................................................... 28 9. $C^1$ solutions.................................................................................. 30 10. Monotonic solutions......................................................................... 35 11. Monotonic solutions of the equation ϱ[f(x)] — ϱ(x) = h(x)........... 36 12. Convex solutions............................................................................... 38 13. Local $C^p$ transformations of the real line............................... 43 14. Iterations and commuting functions.............................................. 45 REFERENCES