We report new observations that combine high-precision infrared polarimetry and high-resolution imagery in the visible to demonstrate that most of the quiet solar surface contains a measurable magnetic field. We found that when observed at 1 arcsec2 resolution, 68% of the observed area contains magnetic flux higher than 5×1015 Mx (corresponding to an apparent average field of 1 G). The majority of these magnetic features have magnetic flux below 5×1016 Mx. Their magnetic field strengths range from below 200 to 1000 G, which means that their filling factors are on the order of 1%. The spatial distribution and time evolution of these magnetic features are closely associated with the solar granulation. The properties of these weak granular magnetic features we observed differ from those of the intranetwork fields described in earlier observations. We also observed the formation and disappearance of a kilogauss magnetic feature associated with the development of intergranular lanes, which may be evidence of convective collapse.