The Adaptive Gain Integrating Pixel Detector (AGIPD) is an X-ray imager,custom designed for the European X-ray Free-Electron Laser (XFEL). It is afast, low-noise integrating detector, with an adaptive gain amplifier per pixel.This has an equivalent noise of less than 1 keV when detecting single photonsand, when switched into another gain state, a dynamic range of more than104photons of 12 keV. In burst mode the system is able to store 352 imageswhile running at up to 6.5 MHz, which is compatible with the 4.5 MHz framerate at the European XFEL. The AGIPD system was installed andcommissioned in August 2017, and successfully used for the first experimentsat the Single Particles, Clusters and Biomolecules (SPB) experimental station atthe European XFEL since September 2017. This paper describes the principalcomponents and performance parameters of the system.