Considering the increasingly large impacts and potentials of cyberworlds as seen in e-financing that trades GDP equivalent in a day, we human beings living in the real world are at the stage of needing to firmly identify the nature of cyberworlds. It is clear that if we continue to deal with cyberworlds as we have been, they grow chaotic beyond human understanding and control, endangering the real world. In an effort to make cyberworlds an academic discipline to overcome the critical situation, we axiomatize cyberworlds and then theorize them as Euclid did in identifying shapes in the real world.