We present results for the matrix elements relevant for proton decay in Grand Unified Theories (GUTs), using two methods. In the indirect method, we rely on an effective field theory description of proton decay, where we need to estimate two low energy constants. We then relate these low energy constants to the proton decay matrix elements using leading order chiral perturbation theory. In the direct method, we calculate the required matrix elements directly; this is computationally more expensive, but the calculation has no systematic error from the use of chiral perturbation theory. The calculations are performed with 2+1 flavors of domain wall fermions on lattices of size 163 × 32 and 243 × 64 with a fifth dimension of length 16. We work at fixed inverse lattice spacing, a−1 = 1.73(3) GeV, leading to physical volumes of (1.8 fm)3 and (2.7 fm)3 for the 163 × 32 and 243 × 64 lattices respectively. In the first four chapters we present the background theory. We start with a brief review of the standard model and the motivation for GUTs. We show that GUTs must lead to proton decay, and that the proton lifetime is an experimentally testable prediction which can be used to constrain GUT parameters, or rule out classes of GUT which predict a minimum lifetime shorter than the experimental minimum bound. We then review continuum and lattice QCD, including outlines of the lattice methods used to calculate the proton decay matrix elements. In the last three chapters we present the results and analysis. We calculate the nucleon and pion two–point correlation functions, and determine their ground state masses and amplitudes. These quantities will then be used to calculate the matrix elements using the indirect and direct methods outlined above. The matrix elements can then be combined with experimental bounds on the proton lifetime to bound parameters of individual GUTs.