After decades of exploration, the martian neutral hydrogen exosphere has remained poorly characterized. The first measurements of this layer by Mariner 6 and 7 revealed it to be optically thick in Lyman α emission, along with a characteristic temperature that was higher than the majority of the collisional atmosphere of Mars. Further exploration revealed that the hydrogen in the martian exosphere was formed from photodissociation of water vapor by solar UV light, and that its escape can be directly linked to the escape of water from Mars. Theoretical analysis of hydrogen transport in the martian atmosphere suggested a steady escape rate limited by diffusion of hydrogen through the martian atmosphere. Subsequent missions to Mars provided a wide range of values for the temperature and density of hydrogen at Mars. It is important to determine the properties of the martian hydrogen exosphere in order to constrain the escape flux, which can then be used to calculate the total amount of water lost by Mars during its evolutionary history. In this dissertation the characteristics of the martian hydrogen exosphere are constrained using data from the Hubble Space Telescope (HST). HST observations of this layer reveal short-term seasonal changes, thereby disproving the theory of constant escape rate for H from Mars. Analysis of these datasets using a radiative transfer model constructed at Boston University revealed a large seasonal variation in the hydrogen escape flux, making it difficult to easily backtrack the martian water loss history. Results also indicate the possible presence of a superthermal population created by non-thermal processes at Mars. Exploration of the latitudinal symmetry of the martian exosphere indicates that it is symmetric above 2.5 martian radii and asymmetric below this altitude, which could be due to temperature differences between the day and night side. Finally, there are large uncertainties in determining the characteristics of the martian exosphere after decades of exploration, due to various assumptions about the intrinsic characteristics of the martian exosphere in the modeling process, degeneracy in the two modeling parameters for hydrogen -i.e. its temperature and density, unaccounted seasonal effects and uncertainties introduced from spacecraft instrumentation and viewing geometry.