Information and randomness

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The first edition of the monograph by Cristian Calude, published in 1994, marked a significant milestone in algorithmic information theory, which has seen vigorous growth in recent years. The book presents original research that enriches the field, making it suitable for both researchers and as a textbook. It is self-contained, with all proofs included, eliminating the need for additional sources in classroom settings. The second edition reflects continued advancements in the study, featuring numerous new results, examples, exercises, and open problems. Notably, it introduces two new chapters: “Computably Enumerable Random Reals” and “Randomness and Incompleteness.” A comprehensive new bibliography enhances its value for researchers. The new findings on computably enumerable random reals and Omega Numbers significantly contribute to its utility as a textbook. The author’s direct involvement in these results, published in prestigious journals like Nature and New Scientist, underscores the book's relevance and impact in the field.