I use N-body simulations of the Milky Way and its satellite population of dwarf galaxies to probe the small-scale power spectrum and the properties of the unknown dark matter particle. The number of dark matter satellites decreases with decreasing mass of the dark matter particle. Assuming that the number of dark matter satellites exceeds or equals the number of observed satellites of the Milky Way, I derive a lower limit on the dark matter particle mass of m_WDM > 2.1 keV for a thermal dark matter particle, with 95% confidence. The recent discovery of many new dark matter dominated satellites of the Milky Way in the Sloan Digital Sky Survey allows me to set a limit comparable to constraints from the complementary methods of Lyman-&alpha forest modeling and X-ray observations of the unresolved cosmic X-ray background and of halos from dwarf galaxy to cluster scales.

I also investigate the claim that the largest subhalos in high resolution dissipationless cold dark matter (CDM) simulations of the Milky Way are dynamically inconsistent with observations of its most luminous satellites. I quantify the effects of the adopted cosmological parameters on the satellite densities and show the tension between observations and simulations adopting parameters consistent with WMAP9 is greatly diminished. I explore warm dark matter (WDM) cosmologies for 1-4 keV thermal relics. In 1 keV cosmologies subhalos have circular velocities at kpc scales 60% lower than their CDM counterparts, but are reduced by only 10% in 4 keV cosmologies. Recent reports of a detected X-ray line in emission from galaxy clusters has been argued as evidence of sterile neutrinos with properties similar to a 2 keV thermal relic. If confirmed, my simulations show they would naturally reconcile the densities of the brightest satellites and be consistent with the abundance of ultra-faint dwarfs.

I conclude by using N-body simulations of a large set of dark matter halos in different CDM and WDM cosmologies to demonstrate that the spherically averaged density profile of dark matter halos has a shape that depends on the power spectrum of initial conditions. Virialization isotropizes the velocity dispersion in the inner regions of the halo but does not erase the memory of the initial conditions in phase space. I confirm that the slope of the inner density profile in CDM cosmologies depends on the halo mass with more massive halos exhibiting steeper profiles. My simulations support analytic models of halo structure that include angular momentum and argue against a universal form for the density profile.