Logarithmic construction of the moduli space of admissible covers

For the thesis project, we are interested in learning about the Harris-Mumford modular compactification of the classical Hurwitz stack using log admissible covers. The Hurwitz stack parametrizes d-sheeted, simple branched coverings of {P}^{1} with b branched points. In this thesis, we present a complete proof of the fact that the stack of log admissible covers is a proper Deligne-Mumford logarithmic stack.