We calculate moments of the generalized parton distributions of the nucleon using lattice QCD. The generalized parton distributions determine the angular momentum decomposition of the nucleon and the transverse distributions of partons within the nucleon. Additionally, the generalized parton distributions reduce to the elastic form factors and ordinary parton distributions in particular kinematic limits. Thus by calculating moments of the generalized parton distributions in lattice QCD we can explore many facets of the structure of the nucleon. In this effort, we have developed the building block method to determine all the lattice correlation functions which con- tribute to the off forward matrix elements of the twist two operators. These matrix elements determine the generalized form factors of the nucleon which in turn give the moments of the generalized parton distributions. Thus we use our building block method to calculate all the matrix elements of the lowest twist two operators. Fur- thermore, we use our method to construct an overdetermined set of matrix elements allowing a more accurate calculation of the generalized form factors.

In this work, we calculate various nucleon structure observables using the fundamental theory of quarks and gluons, QCD, simulated on a lattice. In our simulations, we use the full QCD action including Nf = 2+ 1 dynamical quarks in the SU(2) isospin limit. We compute the nucleon vector and axial vector form factors as well as the generalized form factors, and analyze the nucleon charge, magnetization, and axial radii, anomalous magnetic moment, and axial charge. In addition, we compute quark contributions to the nucleon momentum and spin. Our calculation is novel for three reasons. It is a first full QCD calculation using both sea and valence chiral quarks with pion masses as low as m[pi] = 300 MeV. We develop a method to keep systematic effects in the lattice nucleon matrix elements under control, which helps us to obtain a better signal-to-noise ratio, to achieve higher precision and to test the applicability of low-energy effective theories. Finally, we compare the results from lattice QCD calculations with two different discretization methods and lattice spacings, with the rest of the calculation technique kept equal. The level of agreement between these results indicates that our calculations are not significantly affected by discretization effects.

Since the discovery in the 1960's that the proton is not a fundamental particle but instead composed of even smaller particles known as quarks and gluons, there has been a concerted effort to understand the proton's internal structure. There still remain many mysteries about the proton and the theory that describes the interactions within: Quantum Chromodynamics (QCD). The distributions of quarks and gluons are encoded in objects known as parton correlation functions. Physicists use high-energy scattering experiments to access these functions by means of QCD factorization. This process of extracting information is known as a global QCD analysis. Further insight can be gained through first-principles calculations in lattice QCD as well as models for the strong interaction. In this thesis, we will use global QCD analyses to provide information on the one-dimensional (1D) structure of the proton using the latest experimental data available. Among the mysteries that remain within the proton, we provide insight on the non-perturbative nature of the proton's sea quarks, for both cases where the proton is unpolarized and longitudinally polarized. We also bring new information on the "proton spin puzzle," which concerns the delegation of the proton's spin into its constituent quarks and gluons. We shed light on the proton's transversely polarized structure, where current results from global QCD analyses and lattice QCD fail to paint a consistent picture. Our analyses also reveal a new feature of nuclear effects within light, highly asymmetric nuclei such as helium and tritium. Finally, we perform derivations in a spectator diquark model to glean information on the proton's 3D structure, and calculate moments that can be used in future lattice QCD studies.