This chapter will take us into a world very different from all that we have seen so far concerning Shannon's information theory. As we shall see, it is a strange world made of virtual computers (universal Turing machines) and abstract axioms that can be demonstrated without mathematics merely by the force of logic, as well as relatively involved formalism. If the mere evocation of Shannon, of information theory, or of entropy may raise eyebrows in one's professional circle, how much more so that of Kolmogorov complexity! This chapter will remove some of the mystery surrounding “complexity,” also called “algorithmic entropy,” without pretending to uncover it all. Why address such a subject right here, in the middle of our description of Shannon's information theory? Because, as we shall see, algorithmic entropy and Shannon entropy meet conceptually at some point, to the extent of being asymptotically bounded, even if they come from totally uncorrelated basic assumptions! This remarkable convergence between fields must make integral part of our IT culture, even if this chapter will only provide a flavor. It may be perceived as being somewhat more difficult or demanding than the preceding chapters, but the extra investment, as we believe, is well worth it. In any case, this chapter can be revisited later on, should the reader prefer to keep focused on Shannon's theory and move directly to the next stage, without venturing into the intriguing sidetracks of algorithmic information theory.