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The Atacama pathfinder experiment Sunyaev-Zel'dovich (APEX-SZ) instrument is a millimeter-wave cryogenic receiver designed to observe galaxy clusters via the Sunyaev-Zel'dovich effect from the 12 m APEX telescope on the Atacama plateau in Chile. The receiver contains a focal plane of 280 superconducting transition-edge sensor (TES) bolometers instrumented with a frequency-domain multiplexed readout system. The bolometers are cooled to 280 mK via a three-stage helium sorption refrigerator and a mechanical pulse-tube cooler. Three warm mirrors, two 4 K lenses, and a horn array couple the TES bolometers to the telescope. APEX-SZ observes in a single frequency band at 150 GHz with 1′ angular resolution and a 22′ field-of-view, all well suited for cluster mapping. The APEX-SZ receiver has played a key role in the introduction of several new technologies including TES bolometers, the frequency-domain multiplexed readout, and the use of a pulse-tube cooler with bolometers. As a result of these new technologies, the instrument has a higher instantaneous sensitivity and covers a larger field-of-view than earlier generations of Sunyaev-Zel'dovich instruments. The TES bolometers have a median sensitivity of 890 [formula] (NEy of 3.5 × 10-4 [formula]). We have also demonstrated upgraded detectors with improved sensitivity of 530 [formula] (NEy of 2.2 × 10-4 [formula]). Since its commissioning in April 2007, APEX-SZ has been used to map 48 clusters. We describe the design of the receiver and its performance when installed on the APEX telescope. [ABSTRACT FROM AUTHOR]