The future may reveal new theories of information, which could empower the user with some automatic assessment of the information usefulness or value in terms of scientific, societal, personal, and global impact. Without a shadow of a doubt, this would lead to worrisome information computer, with Internet pervasiveness in both professional and private areas, taking care of everything in order for us not to worry about anything, just like the space companion HAL. This might also change the face of the Internet, with more and more intelligent browsers and search engines to present us the information the way we may appreciate it the most. Maybe we are not that far from such a frightening reality. Nevertheless, this only remains a matter of philosophical debate and speculation. To close this preliminary discussion, we may simply conclude that information theory is neutral about information content and its subjective value. Its purpose is to derive mathematical algorithms for measuring, coding, and processing information, as reduced to immaterial data. The rest of this chapter is dedicated to the issue of measuring information, which is central to information theory. The nice and exciting thing indeed, is that information can be measured, and this will be our starting point in the information- theory journey. Measuring information Haven't we experienced rushing to the mailbox, the newsstand, or the TV? This excep- tional interest in the mail or the news has many possible reasons: appointment confir- mation, contract signature, conclusion of litigation, events of nationwide impact, such as disasters, elections, sports, but also house hunting, job classifieds, favorite rubrics, 3.2 Measuring information or, for children, Sunday cartoons! We have all also noticed that the value attributed to the mail or the newspaper decreases relatively quickly. Once read, both usually go to the recycling bin. This indicates that the information in these types of news has a special meaning in terms of being new or unexpected, which shar