Résumé : The First G-APD Cherenkov Telescope (FACT) is an Imaging Air Cherenkov Telescope located on the Canary Island of La Palma. It is the first of its kind which uses Geiger-mode Avalanche Photo Diodes (G-APDs) as photosensors to detect the Cherenkov radiation emitted from secondary particles in a high-energy gamma-ray air shower. A new analysis chain has been developed using modern data mining methods and unfolding techniques to obtain the energy spectrum of an observed source. This analysis chain has been applied to data of the Crab Nebula, the so called 'standard candle' in Cherenkov astronomy. Here, the individual steps are described and results of this application are reported providing the energy spectrum and light curve.