Gauge theories are the basis of modern theories of high-energy physics. Perturbative calculations are crucial to developing our quantitative understanding of these theories, as well as seeking new and deeper structures in these theories. Precision higher-order calculations in the SU(3) component of the Standard Model, perturbative Quantum Chromodynamics (QCD), will be crucial to understanding data at the CERN-based Large Hadron Collider (LHC) and finding and measuring physics beyond the standard model. Precision calculations in the electroweak theory will also play a role in confronting later precision data with theoretical models. The related maximally (N=4) supersymmetric gauge theory has served both as an important theoretical laboratory for developing new calculational techniques, as well as a link to string theory via the AdS/CFT duality. It is also emerging as a fruitful meeting point for ideas and methods from three distinct areas of theoretical physics: perturbative gauge theories, integrable systems, and string theory. The Project covers three related areas of perturbative gauge theories: computation of one- and two-loop amplitudes in perturbative quantum chromodynamics; incorporation of these amplitudes and development of a fully-matched parton-shower formalism and numerical code; and higher-loop computations in the N=4 supersymmetric theory. It aims to develop a general-purpose numerical-analytic hybrid program for computing phenomenologically-relevant one- and two-loop amplitudes in perturbative QCD. It also aims to develop a new parton shower allowing complete matching to leading and next-to-leading order computations. It seeks to further develop on-shell computational methods, and apply them to the N=4 supersymmetric gauge theory, with the goal of connecting perturbative quantities to their strong-coupling counterparts computed using the dual string theory.