BABAR, the detector for the SLAC PEP-II asymmetric e+e− B Factory operating at the ϒ(4S) resonance, was designed to allow comprehensive studies of CP-violation in B-meson decays. Charged particle tracks are measured in a multi-layer silicon vertex tracker surrounded by a cylindrical wire drift chamber. Electromagnetic showers from electrons and photons are detected in an array of CsI crystals located just inside the solenoidal coil of a superconducting magnet. Muons and neutral hadrons are identified by arrays of resistive plate chambers inserted into gaps in the steel flux return of the magnet. Charged hadrons are identified by dE/dx measurements in the tracking detectors and by a ring-imaging Cherenkov detector surrounding the drift chamber. The trigger, data acquisition and data-monitoring systems, VME- and network-based, are controlled by custom-designed online software. Details of the layout and performance of the detector components and their associated electronics and software are presented.