We present the first fully self-consistent, axisymmetric, dynamical model of the Andromeda galaxy (M31). We constrain the physical parameters of the model with datasets on all radial scales: the bulge projected velocity dispersion, rotation curve, surface brightness profile, and the kinematics of globular clusters and satellite galaxies. Combining these highly heterogeneous datasets into a single self-consistent analysis is natural in the framework of Bayesian inference. Using a geometric argument, we also infer the three-dimensional velocity of M31 relative to the Milky Way. From this orbit, we constrain the total mass of the Local Group by the ``timing argument''. We find that the virial mass of M31 is $M_\mathrm{M31,vir} = 5.0^{+2.2}_{-1.7} \times 10^{12} \, M_\odot$ and the mass of the Local Group is $M_\mathrm{LG} = 8.8^{+8.0}_{-4.2} \times 10^{12} \, M_\odot$. We conclude that the large uncertainties in our results are due primarily to the small sample size at large radii and that either a significantly larger sample or unjustifiably informative priors are necessary to improve the constraint. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2010-08-27 08:32:52.823