  We survey the Kolmogorov's approach to the notion of randomness through the
Kolmogorov complexity theory. The original motivation of Kolmogorov was to give
up a quantitative definition of information. In this theory, an object is
randomness in the sense that it has a large information content. Afterwards, we
present parts of the work of Martin-Lof, Schnorr, Chaitin and Levin which
supply a mathematical notion of randomness throughout diverse theories from the
the 60' up to recently.
