  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 Kolmogorov's
and Shannon's 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 Occam's razor in inductive inference.
We end by discussing some of the philosophical implications of the theory.
