Las Cumbres Observatory Global Telescope (LCOGT) is a young organization dedicated to time-domain observations at optical and (potentially) near-IR wavelengths. To this end, LCOGT is constructing a worldwide network of telescopes, including the two 2 m Faulkes telescopes, as many as 17 × 1 m telescopes, and as many as 23 × 40 cm telescopes. These telescopes initially will be outfitted for imaging and (excepting the 40 cm telescopes) spectroscopy at wavelengths between the atmospheric UV cutoff and the roughly 1-μm limit of silicon detectors. Since the first of LCOGT's 1 m telescopes are now being deployed, we lay out here LCOGT's scientific goals and the requirements that these goals place on network architecture and performance, we summarize the network's present and projected level of development, and we describe our expected schedule for completing it. In the bulk of the paper, we describe in detail the technical approaches that we have adopted to attain desired performance. In particular, we discuss our choices for the number and location of network sites, for the number and sizes of telescopes, for the specifications of the first generation of instruments, for the software that will schedule and control the network's telescopes and reduce and archive its data, and for the structure of the scientific and educational programs for which the network will provide observations.