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Recently, there has been growing interest in exploring the limits to scaling of semiconductor devices, and in understanding their characteristics in the regime where quantum effects and ballistic transport dominate. Using high-resolution fabrication techniques on high-mobility, modulation-doped AlGaAs/GaAs, it is possible to confine the two-dimensional electron gas (2DEG) to structures that are smaller than both the inelastic and elastic scattering lengths, and are comparable in size to the electron wavelength. The conduction of such a device should be one dimensional and ballistic. Unlike large samples, the resistance of these ballistic devices does not follow classical equations; it is primarily caused by electron interference and scattering from the geometry of the sample, not by impurities. On this scale, these structures behave as electron waveguides not as diffusive conductors. We have used electron-beam lithography and high-resolution reaction ion etching to produce samples with well controlled, complicated geometries. These devices use either depletion from an etched surface, or the application of a gate voltage to electrostatically confine the 2DEG to a narrow conducting channel. Transport measurements exhibit electron interference effects, nonlocal resistance fluctuations, resistance that does not scale with length, and quantization-of-resistance as a function of width and carrier density. The experiments correspond well to theoretical calculations of simple electron waveguides, and show that in these one-dimensional ballistic devices, the measured resistance is primarily caused by scattering from the structure of the sample itself.