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LiFePO4 in the olivine structure is a promising cathode material for Li ion batteries. During normal battery operation, an olivine form of FePO4 is produced. In addition to the olivine form, FePO4 is known to form in a quartz-like structure, a high pressure CrVO4-like structure, and a monoclinic structure. We report the results of a detailed density functional study of the electronic structures and total energies of these four crystalline structures of FePO4. Partial density of states analysis of the four materials finds them all to be characterized by strong hybridization between the Fe and O contributions throughout their upper valence bands, consistent with recent X-ray spectroscopy studies of olivine FePO4. Results obtained using the local density approximation for the exchange-correlation functional find the olivine structure to be more stable than the quartz-like stucture by 0.1 eV which is in good agreement with recent calorimetry experiments.