The Boston University-Five College Radio Astronomy Observatory Galactic Ring Survey is a new survey of Galactic (CO)-C-13 J = 1 -> 0 emission. The survey used the SEQUOIA multipixel array on the Five College Radio Astronomy Observatory 14 m telescope to cover a longitude range of l = 18 degrees 55 degrees.7 and a latitude range of vertical bar b vertical bar < 1 degrees, a total of 75.4 deg(2). Using both position-switching and On-The-Fly mapping modes, we achieved an angular sampling of 2200, better than half of the telescope's 4600 angular resolution. The survey's velocity coverage is -5 to 135 km s(-1) for Galactic longitudes l <= 40 degrees and -5 to 85 km s(-1) for Galactic longitudes l > 40 degrees. At the velocity resolution of 0.21 km s(-1), the typical rms sensitivity is sigma(T*(Alpha)) similar to 0.13 K. The survey comprises a total of 1,993,522 spectra. We show integrated intensity images (zeroth moment maps), channel maps, position-velocity diagrams, and an average spectrum of the completed survey data set. We also discuss the telescope and instrumental parameters, the observing modes, the data reduction processes, and the emission and noise characteristics of the data set. The Galactic Ring Survey data are available to the community online or in DVD form by request.