AGIPD is a hybrid pixel detector developed by DESY, PSI, and the Universities of Bonn and Hamburg. It is targeted for use at the European XFEL, a source with unique properties: a train of up to 2700 pulses is repeated at 10 Hz rate. The pulses inside a train are ≤100fs long and separated by 220 ns, containing up to 10¹² photons of 12.4 keV each. The readout ASICs with 64 x 64 pixels each have to cope with these properties: Single photon sensitivity and a dynamic range up to 10⁴ photons/pixel in the same image as well as storage for as many as possible images of a pulse train for delayed readout, prior to the next train. The high impinging photon flux also requires a very radiation hard design of sensor and ASIC, which uses 130 nm CMOS technology and radiation tolerant techniques. The signal path inside a pixel of the ASIC consists of a charge sensitive preamplifier with 3 individual gains, adaptively selected by a subsequent discriminator. The preamp also feeds to a correlated double sampling stage, which writes to an analogue memory to record 352 frames. It is random-access, so it can be used most efficiently by overwriting bad or empty images. Encoded gain information is stored to a similar memory. Readout of these memories is via a common charge sensitive amplifier in each pixel, and multiplexers on four differential ports. Operation of the ASIC is controlled via a command interface, using 3 LVDS lines. It also serves to configure the chip's operational parameters and timings.