The Cosmic Microwave Background has proven to be an invaluable tool for cosmology, but much of the scientific information contained in its polarization anisotropy is still to be discovered. Of particular interest is the angular power spectrum of the tiny B-mode polarization signal, the divergence free component which is geometrically distinct from the dominant E-modes. The theory of inflation, which has been proposed to explain several curious features of our universe, predicts the existence of B-mode fluctuations on large angular scales and at a signal level that may be achievable in the near future.The Q/U Imaging Experiment (QUIET) is designed to make sensitive measurements of the CMB polarization using arrays of integrated "detectors on a chip" that can be scaled to reach the sensitivity requirements for detecting B-modes.This thesis covers the design of QUIET, which consists of separate instruments for observation at 40 and 90 GHz. After the discussion of the detectors, which generally applies to both instruments, the remaining sections focus on observations, calibration, and data analysis for the 40 GHz detector. Tests performed on the data indicate some not-yet-identified source of contamination that must be understood and corrected before a reliable result can be obtained.
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