The goal of the GlueX experiment is to provide critical data needed to address one of the outstanding and fundamental challenges in physics -- the quantitative understanding of the confinement of quarks and gluons in quantum chromodynamics (QCD). Confinement is a unique property of QCD and understanding confinement requires an understanding of the soft gluonic field responsible for binding quarks in hadrons. Hybrid mesons, and in particular exotic hybrid mesons, provide the ideal laboratory for testing QCD in the confinement regime since these mesons explicitly manifest the gluonic degrees of freedom. Photoproduction is expected to be particularly effective in producing exotic hybrids but there is little data on the photoproduction of light mesons. GlueX will use the coherent bremsstrahlung technique to produce a linearly polarized photon beam. A solenoid-based hermetic detector will be used to collect data on meson production and decays with statistics after the first year of running that will exceed the current photoproduction data in hand by several orders of magnitude. These data will also be used to study the spectrum of conventional mesons, including the poorly understood excited vector mesons. In order to reach the ideal photon energy of 9 GeV for this mapping of the exotic spectrum, 12 GeV electrons are required. This document describes the physics goals, the beam and apparatus, and plans for the first two years of commissioning and data-taking.