The quest for the revelation of the deepest composition of the structure of matter and the nature of the fundamental forces that bind them together is underway, using experiments with colliding hadron beams at the largest energy and luminosity that present and near-future accelerator technology can allow. This book gives the physics motivation of such a collider and discusses the benefits and requirements of the experimental program. Obviously the size of the collider is a major concern, and that is determined by the bending field which is possible to achieve in superconducting magnets; the book includes a discussion on the ultimate expected magnetic field that can be reached. There are also presentations of straw-man designs; in particular, the effects of the synchrotron radiation, which are quite significant at very large energies and large bending fields, are examined, with the possibility of taking advantage of them for the attainment of small beam size and thus luminosity. In addition, detector issues are discussed, especially in relation to the large expected background, the total number of events, and the difficulties of gathering and selecting relevant events. Finally, there is a discussion on the social and political implications of such a project.