Abstract : The Large Area Telescope (LAT), to be launched in 2006 on the GLAST space mission, will undertake gamma-ray astronomy in the energy range 30 MeV to 300 GeV. The LAT sky survey will have 20 times greater sensitivity, and broader energy coverage, than EGRET did. Projections from the EGRET results indicate that GLAST will detect thousands of sources. The calorimeter section of GLAST is segmented and layered, which permits shower profiles to be measured and good determinations of gamma-ray energies even when showers are not completely contained. Owing to the thinness of the calorimeter, shower leakage can be significant even at energies as low as 1 GeV. Using simulations and data from beam tests we developed reconstruction methods adapted to the various incident energies and angles including corrections for losses in the tracker and for longitudinal leakage. The resulting performance is described here. We also present position estimation in such a calorimeter and discuss some intrinsic biases. Because of the large number of sources, the need to monitor the data constantly for flaring sources, and the possibility to observe extended objects with the LAT, some innovative source detection methods are needed. We propose a method based on wavelet analysis, well adapted to the bright and highly structured background of diffuse gamma-ray emission from cosmic-ray interactions with interstellar gas and photons in the Milky Way. The wavelet transform statistic is detailed. This method has been tested on EGRET data and we discuss its application to GLAST. Finally, we propose to use GLAST as a very high energy (from a few hundred GeV to a few TeV) cosmic electron telescope. We discuss the importance of measuring the spectrum of the cosmic-ray electrons and detail the capabilities of GLAST. The classical approach to the origin of local electrons is criticized and a simple model of the acceleration and escape of electrons in supernovae remnants is presented.