This book offers a comprehensive introduction to algorithmic information theory: it defines plain and prefix Kolmogorov complexity, explains the incompressibility method, relates complexity to Shannon information, and develops tests of randomness culminating in Martin-Löf randomness and Chaitin’s Ω. It surveys links to computability theory, mutual information, algorithmic statistics, Hausdorff dimension, ergodic theory, and data compression, providing numerous exercises and historical notes. By unifying complexity and randomness, it supplies rigorous tools for measuring information content, proving combinatorial lower bounds, and formalizing the notion of random infinite sequences, thus shaping modern theoretical computer science.
