  The Transition Radiation Detector (TRD) was designed and built to enhance the
capabilities of the ALICE detector at the Large Hadron Collider (LHC). While
aimed at providing electron identification and triggering, the TRD also
contributes significantly to the track reconstruction and calibration in the
central barrel of ALICE. In this paper the design, construction, operation, and
performance of this detector are discussed. A pion rejection factor of up to
410 is achieved at a momentum of 1 GeV/$c$ in p-Pb collisions and the
resolution at high transverse momentum improves by about 40% when including the
TRD information in track reconstruction. The triggering capability is
demonstrated both for jet, light nuclei, and electron selection.
