Nearly all galaxies in the Universe are formed around a scaffolding of invisible matter. Without its mass providing gravitational glue, the Milky Way, for example, would rip itself apart. This mysterious substance is called dark matter, and it makes up 85% of the mass of the Universe, but physicists have yet to discover its true nature. If dark matter is made of particles, what kind of particles are they? How does it interact with regular matter? And how does dark matter fit into the history of the Universe? Using the computational method of lattice field theory, I study Stealth Dark Matter, a type of dark matter made of composite particles similar to protons and neutrons. I will discuss how Stealth Dark Matter can answer each of the questions above, and I will describe my study of Stealth Dark Matter self-interactions and their role in galaxy formation.