@TechReport{ it:2000-034, author = {Alexander Shen}, title = {Algorithmic Information Theory and Kolmogorov Complexity}, institution = {Department of Information Technology, Uppsala University, and Independent University of Moscow, Russia}, department = {Computing Science Division}, year = {2000}, number = {2000-034}, month = dec, abstract = {This document contains lecture notes of an introductory course on Kolmogorov complexity. They cover basic notions of algorithmic information theory: Kolmogorov complexity (plain, conditional, prefix), notion of randomness (Martin-Lof randomness, Mises-Church randomness), Solomonoff universal a priori probability and their properties (symmetry of information, connection between a priori probability and prefix complexity, criterion of randomness in terms of complexity) and applications (incompressibility method in computational complexity theory, incompleteness theorems). } }