The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events

In this paper we describe in detail the design considerations for this detector for operation in the extreme multiplicity environment of central Pb-Pb collisions at LHC energy. The implementation of the resulting requirements into hardware (field cage, read-out chambers, electronics), infrastructure (gas and cooling system, laser-calibration system), and software led to many technical innovations which are described along with a presentation of all the major components of the detector, as currently realized. We also report on the performance achieved after completion of the first round of stand-alone calibration runs and demonstrate results close to those specified in the TPC Technical Design Report.