Magnetic reconnection is a fundamental physical process involving rapid changes in magnetic field topology that is thought to be responsible for energetic outbursts in astrophysical and laboratory plasmas. Often described as a breakdown of ideal magnetohydrodynamics, magnetic reconnection is a complex process with competing mathematical theories and unresolved questions surrounding rates at which field topology changes, mechanisms for energy conversion and applicability to a range of astrophysical and laboratory problems. I developed and validated a Hall magnetohydrodynamics module for the Athena++ code and studied properties of Hall reconnection as a function of of mathematical formulations for global plasma dynamics, theoretical models for reconnection, and initial conditions.