One of the primary drivers in the development of large format millimeter detector arrays is the study of sub-millimeter galaxies (SMGs) - a population of very luminous high-redshift dust-obscured starbursts that are widely believed to be the dominant contributor to the Far-Infrared Background (FIB). The characterization of such a population requires the ability to map large patches of the (sub-)millimeter sky to high sensitivity within a feasible amount of time. I present this dissertation on the design, integration, and characterization of the 144-pixel AzTEC millimeter-wave camera and its application to the study of the sub-millimeter galaxy population. In particular, I present an unprecedented characterization of the "blank-field" (fields with no known mass bias) SMG number counts by mapping over 0.5 deg 2 to 1.1mm depths of ∼1mJy - a previously unattained depth on these scales. This survey provides the tightest SMG number counts available, particularly for the brightest and rarest SMGs that require large survey areas for a significant number of detections. These counts are compared to the predictions of various models of the evolving mm/sub-mm source population, providing important constraints for the ongoing refinement of semi-analytic and hydrodynamical models of galaxy formation. I also present the results of an AzTEC 0.15 deg 2 survey of the COSMOS field, which uncovers a significant over-density of bright SMGs that are spatially correlated to foreground mass structures, presumably as a result of gravitational lensing. Finally, I compare the results of the available SMG surveys completed to date and explore the effects of cosmic variance on the interpretation of individual surveys.