The aim of this talk is twofold - to give a taste of how simple ideas can help study the homotopy type of complicated simplicial complexes, and to introduce the Steinberg module. The Steinberg module is an important representation of the General Linear Group that helps study its cohomology, and can be defined in terms of a certain simplicial complex. We will build up towards defining this complex and proving the Solomon-Tits theorem that shows it is highly connected. If time permits, we shall also see a construction by Lee-Szczarba that builds a resolution of the Steinberg module by analyzing a simplicial complex.