Particle accelerators enable scientists to study the fundamental structure of the universe, but have become the largest and most expensive of scientific instruments. In this project, we advanced the science and technology of laser-plasma accelerators, which are thousands of times smaller and less expensive than their conventional counterparts. In a laser-plasma accelerator, a powerful laser pulse exerts light pressure on an ionized gas, or plasma, thereby driving an electron density wave, which resembles the wake behind a boat. Electrostatic fields within this plasma wake reach tens of billions of volts per meter, fields far stronger than ordinary non-plasma matter (such as the matter that a conventional accelerator is made of) can withstand. Under the right conditions, stray electrons from the surrounding plasma become trapped within these "wake-fields", surf them, and acquire energy much faster than is possible in a conventional accelerator. Laser-plasma accelerators thus might herald a new generation of compact, low-cost accelerators for future particle physics, x-ray and medical research. In this project, we made two major advances in the science of laser-plasma accelerators. The first of these was to accelerate electrons beyond 1 gigaelectronvolt (1 GeV) for the first time. In experimental results reported in Nature Communications in 2013, about 1 billion electrons were captured from a tenuous plasma (about 1/100 of atmosphere density) and accelerated to 2 GeV within about one inch, while maintaining less than 5% energy spread, and spreading out less than 1/2 milliradian (i.e. 1/2 millimeter per meter of travel). Low energy spread and high beam collimation are important for applications of accelerators as coherent x-ray sources or particle colliders. This advance was made possible by exploiting unique properties of the Texas Petawatt Laser, a powerful laser at the University of Texas at Austin that produces pulses of 150 femtoseconds (1 femtosecond is 10-15 seconds) in duration and 150 Joules in energy (equivalent to the muzzle energy of a small pistol bullet). This duration was well matched to the natural electron density oscillation period of plasma of 1/100 atmospheric density, enabling efficient excitation of a plasma wake, while this energy was sufficient to drive a high-amplitude wake of the right shape to produce an energetic, collimated electron beam. Continuing research is aimed at increasing electron energy even further, increasing the number of electrons captured and accelerated, and developing applications of the compact, multi-GeV accelerator as a coherent, hard x-ray source for materials science, biomedical imaging and homeland security applications. The second major advance under this project was to develop new methods of visualizing the laser-driven plasma wake structures that underlie laser-plasma accelerators. Visualizing these structures is essential to understanding, optimizing and scaling laser-plasma accelerators. Yet prior to work under this project, computer simulations based on estimated initial conditions were the sole source of detailed knowledge of the complex, evolving internal structure of laser-driven plasma wakes. In this project we developed and demonstrated a suite of optical visualization methods based on well-known methods such as holography, streak cameras, and coherence tomography, but adapted to the ultrafast, light-speed, microscopic world of laser-driven plasma wakes. Our methods output images of laser-driven plasma structures in a single laser shot. We first reported snapshots of low-amplitude laser wakes in Nature Physics in 2006. We subsequently reported images of high-amplitude laser-driven plasma "bubbles", which are important for producing electron beams with low energy spread, in Physical Review Letters in 2010. More recently, we have figured out how to image laser-driven structures that change shape while propagating in a single laser shot. The latter techniques, which use t ...