The Boston University-Five College Radio Astronomy Observatory (BU-FCRAO) Galactic Ring Survey (GRS) of ^13^CO J=1->0 emission covers Galactic longitudes 18<l<55.7{deg} and Galactic latitudes |b|<=1{deg}. Using the SEQUOIA array on the FCRAO 14m telescope, the GRS fully sampled the ^13^CO Galactic emission (46" angular resolution on a 22" grid) and achieved a spectral resolution of 0.21km/s. Because the GRS uses ^13^CO, an optically thin tracer, rather than ^12^CO, an optically thick tracer, the GRS allows a much better determination of column density and also a cleaner separation of velocity components along a line of sight. With this homogeneous, fully sampled survey of ^13^CO emission, we have identified 829 molecular clouds and 6124 clumps throughout the inner Galaxy using the CLUMPFIND algorithm. Here we present details of the catalog and a preliminary analysis of the properties of the molecular clouds and their clumps. Moreover, we compare clouds inside and outside of the 5kpc ring and find that clouds within the ring typically have warmer temperatures, higher column densities, larger areas, and more clumps compared with clouds located outside the ring. This is expected if these clouds are actively forming stars. This catalog provides a useful tool for the study of molecular clouds and their embedded young stellar objects.