The Giant Magellan Telescope adaptive optics system will be an integral part of the telescope, providing laser guide star generation, wavefront sensing, and wavefront correction to most of the currently envisioned instruments. The system will provide three observing modes: Natural Guidestar AO (NGSAO), Laser Tomography AO (LTAO), and Ground Layer AO (GLAO). Every AO observing mode will use the telescope's segmented adaptive secondary mirror to deliver a corrected beam directly to the instruments. High-order wavefront sensing for the NGSAO and LTAO modes is provided by a set of wavefront sensors replicated for each instrument and fed by visible light reflected off the cryostat window. An infrared natural guidestar wavefront sensor with open-loop AO correction is also required to sense tip-tilt, focus, segment piston, and dynamic calibration errors in the LTAO mode. GLAO mode wavefront sensing is provided by laser guidestars over a ∼5 arcminute field of view, and natural guidestars over wider fields. A laser guidestar facility will project 120 W of 589 nm laser light in 6 beacons from the periphery of the primary mirror. An off-axis phasing camera and primary and secondary mirror metrology systems will ensure that the telescope optics remain phased. We describe the system requirements, overall architecture, and innovative solutions found to the challenges presented by high-order AO on a segmented extremely large telescope. Further details may be found in specific papers on each of the observing modes and major subsystems.