Shannon's information theory is based on the concept of probability. Indeed, in that theory, it is random variables who carry information. In the beginning of the 1960s Kolmogorov announced a program of reconstructing Information Theory on the basis of computability, more exactly on the basis of so-called Kolmogorov complexity. Kolmogorov, or descriptional, complexity is the complexity of an object as opposed to computational complexity which is the complexity of a process. Main Kolmogorov's idea reflected an understanding that the more complex an object was, the greater information it contained. So the basic notions and facts of the theory of information got a new interpretation. Parallel studies of both interpretations (Shannon's one and Kolmogorov's one) have led to the notion of information space.