Algorithmic information theory

We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information. We discuss the extent to which Kolmogorovs and Shannons information theory have a common purpose, and where they are fundamentally different. We indicate how recent developments within the theory allow one to formally distinguish between `structural (meaningful) and `random information as measured by the Kolmogorov structure function, which leads to a mathematical formalization of Occams razor in inductive inference. We end by discussing some of the philosophical implications of the theory.