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We survey diverse approaches to the notion of information: from Shannonentropy to Kolmogorov complexity. Two of the main applications of Kolmogorovcomplexity are presented: randomness and classification. The survey is dividedin two parts in the same volume. Part I is dedicated to information theory andthe mathematical formalization of randomness based on Kolmogorov complexity.This last application goes back to the 60's and 70's with the work ofMartin-L\"of, Schnorr, Chaitin, Levin, and has gained new impetus in the lastyears.

Kolmogorov Complexity in perspective. Part I: Information Theory and Randomnes