The field of gamma-ray astronomy has expanded rapidly during the last decade. In the energy regime from 100 GeV up to several TeV, Imaging Atmospheric Cherenkov Telescopes (IACT) are the most sensitive detectors. Presently all IACTs use photomultiplier tubes for light detection, but for future projects Geiger-mode Avalanche Photodiodes (G-APD) are very promising alternatives. In order to demonstrate their potential, the First G-APD Cherenkov Telescope (FACT) collaboration has constructed an IACT camera comprising 1440 G-APDs. By means of specially designed light concentrators the collection area of each sensor is enlarged. The entire electronics for analog signal processing, digitization and triggering is fully integrated into the camera body. Event data are sent via Ethernet to the counting house. The FACT camera was installed during fall 2011 at the Observatorio del Roque de los Muchachos on La Palma, Canary Islands (Spain), on a refurbished telescope mount.