Book Review: An introduction to Kolmogorov Complexity and its Applications Second Edition, 1997 by Ming Li and Paul Vitanyi (Springer (Graduate Text Series))

Chapter 1 contains motivation for the subject and a quick review of combinatorics, probability, and computability. The t reatment is a good refresher course, but is too mature for a first t ime learner. Chapter 2 defines the complexity of a string and some notions of randomness. Informally, the complexity of a string x is the shortest description of x. We give a formal definition that is equivalent to the one in the book.