This thesis describes early work in the developing field of 21-cm intensity mapping. The 21-cm line is a radio transition due to the hyperfine splitting of the ground state of neutral hydrogen (HI). Intensity mapping utilizes the aggregate redshifted 21-cm emission to map the three-dimensional distribution of HI on large scales. In principle, the 21-cm line can be utilized to map most of the volume of the observable Universe. But the signal is small, and dedicated instruments will be required to reach a high signal-to-noise ratio. Large spectrally smooth astrophysical foregrounds, which dwarf the 21-cm signal, present a significant challenge to the data analysis. I derive the fundamental physics of the 21-cm line and the size of the expected cosmological signal. I also provide an overview of the desired characteristics of a dedicated 21-cm instrument, and I list some instruments that are coming on-line in the next few years. I then describe the data analysis techniques and results for 21-cm intensity maps that were made with two existing radio telescopes, the Green Bank telescope (GBT) and the Parkes telescope. Both observations have detected the 21-cm HI signal by cross-correlating the 21-cm intensity maps with overlapping optical galaxy surveys. The GBT maps have been used to constrain the neutral hydrogen density at a mean redshift (z) of 0.8. The Parkes maps, at a mean redshift of 0.08, probe smaller scales. The Parkes 21-cm intensity maps reveal a lack of small-scale clustering when they are cross-correlated with 2dF optical galaxy maps. This lack of small-scale clustering is partially due to a scale-dependent and galaxy-color-dependent HI-galaxy cross- correlation coefficient. Lastly, I provide an overview of planned future analyses with the Parkes maps, with a proposed multi-beam receiver for the Green Bank telescope, and with simulations of systematic effects on foregrounds.
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