ALICE is a general-purpose heavy-ion experiment designed to study the physics of strongly interacting matter and the quark-gluon plasma in nucleus-nucleus collisions at the LHC. It currently involves more than 900 physicists and senior engineers, from both the nuclear and high-energy physics sectors, from over 90 institutions in about 30 countries. The ALICE detector is designed to cope with the highest particle multiplicities above those anticipated for Pb-Pb collisions (dNch/dy up to 8000) and it will be operational at the start-up of the LHC. In addition to heavy systems, the ALICE Collaboration will study collisions of lower-mass ions, which are a means of varying the energy density, and protons (both pp and pA), which primarily provide reference data for the nucleus-nucleus collisions. In addition, the pp data will allow for a number of genuine pp physics studies. The detailed design of the different detector systems has been laid down in a number of Technical Design Reports issued between mid-1998 and the end of 2004...