This volume is the last of three volumes devoted to the work of one of the most prominent 20th century mathematicians. Throughout his mathematical work, A.N. Kolmogorov (1903-1987) showed great creativity and versatility and his wide-ranging studies in many different areas, led to the solution of conceptual and fundamental problems and the posing of new, important questions. His lasting contributions embrace probability theory and statistics, the theory of dynamical systems, mathematical logic, geometry and topology, the theory of functions and functional analysis, classical mechanics, the theory of turbulence, and information theory. This third volume contains original papers dealing with information theory and the theory of algorithms. Comments on these papers are included. The material appearing in each volume was selected by A.N. Kolmogorov himself and is accompanied by short introductory notes and commentaries which reflect upon the influence of this work on the development of modern mathematics. All papers appear in English - some for the first time - and in chronological order. This volume contains a significant legacy which will find many grateful beneficiaries amongst researchers and students of mathematics and mechanics, as well as historians of mathematics.