Abstract : The Fermi Gamma-ray Space Telescope (FGST) has opened a new high-energy window in the study of Gamma-Ray Bursts (GRBs). Here we present a thorough analysis of GRB 080825C, which triggered the Fermi Gamma-ray Burst Monitor (GBM), and was the first firm detection of a GRB by the Fermi Large Area Telescope (LAT). We discuss the LAT event selections, background estimation, significance calculations, and localization for Fermi GRBs in general and GRB 080825C in particular. We show the results of temporal and time-resolved spectral analysis of the GBM and LAT data. We also present some theoretical interpretation of GRB 080825C observations as well as some common features observed in other LAT GRBs.