Thesis advisor: Benjamin Howard / This dissertation gives a description of the GL(4) Rapoport-Zink space, including the connected components, irreducible components, intersection behavior of the irreducible components, and Ekedahl-Oort stratification. As an application of this, this dissertation also includes a description of the supersingular locus of the Shimura variety for the group GU(2,2) over a prime split in the relevant imaginary quadratic field. / Thesis (PhD) — Boston College, 2019. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.