Dark matter is elusive despite making up ~25% of the mass budget of the Universe. It does not interact with the electromagnetic spectrum and can only be measured through its gravitational effects. In the Standard Cosmological Model, Lambda Cold Dark Matter (LCDM), these effects are expected to be present in the largest and smallest galaxies throughout the Universe. Many of these larger systems have had their dark matter content disrupted due to mechanisms predicted by LCDM. We must, therefore, look towards the smaller scales of dwarf galaxies, where this mysterious matter is more likely to remain undisturbed. While LCDM has been remarkable at describing large-scale Universal structure, it has had notable tensions at smaller scales. These are most apparent when comparing observations with simulations of small galaxies, the latter of which can only be best-informed by the former. As technology has improved, so has our view of the Local Group of systems. Over the past three decades, we have been able to expand surveys past the Milky Way and analyze the dwarfs around our neighboring galaxy, Andromeda (M31). In doing so, we have better constrained the effects of and on dark matter, reducing tensions in the Standard Cosmology.

In this thesis, I update the kinematics and estimate the central dark matter densities of several M31 satellite dwarf galaxies. Firstly, I present dynamical mass modeling results of Andromeda (And) VI and Andromeda XXIII and find that And VI is the first mass-modeled M31 dwarf to have a high central dark matter density, as expected in the LCDM paradigm. Conversely, I find that And XXIII joins a growing number of M31 dwarfs estimated to have a lower-than-expected central dark matter density. And XXIII has likely been tidally disrupted and, therefore, has had its dark matter stripped away or expelled. Secondly, I extend my analysis to seven additional M31 satellites and present their mass-modeled results. I find that five of these systems (And I, And VII, And IX, Lacerta I, Cassiopeia III) have lower-than-expected central dark matter densities, while both And III and And V appear to have retained much of their dark matter content. I discuss the role of star formation in creating the estimated densities for all systems and further explore the additional effects of tides on lower-density dwarfs. Finally, I review the most extended, diffuse M31 dwarf galaxy: And XIX. Informed by previous analyses of the system, I present a dark matter density profile for the system. In doing so, I enable more convincing evidence of a significant tidal history, similar to two tidally-disrupted systems around the Milky Way. These chapters build upon the foundation of previous mass modeling analyses of M31 satellites and seek to improve our understanding of dark matter. Modeling of nearby M31 and Milky Way dwarfs will improve our understanding of galaxy evolution and prove crucial to the analysis of more distant, faint systems revealed through increasingly powerful astronomical surveys.