Silicon monoxide (SiO) maser emission has been observed towards many late-type stars. The conditions necessary for the formation of SiO masers dictate that they be produced in a region which is inside the silicate dust formation point close to the surface of the star. Very Long Baseline Interferometry (VLBI) has shown that these masers do indeed lie close to the stellar surface at a distance of a few stellar radii. This extended atmosphere is a complex region dominated by stellar pulsations and permeated by circumstellar shocks. This dissertation presents the results of a multi-epoch VLBI study of the v=1, J=1-0, 43-GHz SiO maser emission towards the symbiotic binary R Aquarii. Four epochs of full-polarization observations were recorded using the Very Long Baseline Array a facility the National Radio Astronomy Observatory. The first high-resolution images of the extended atmosphere of a Mira variable in a symbiotic binary have been produced. The SiO masers towards R Aquarii have been found to exhibit a ring-like morphology ~31 mas (~6.8 AU) in diameter. The emission changes significantly over a time period of ~1-2 months with almost no similarity in structure on timescales >6 months. An analysis of the four epochs of observations has provided the first direct evidence of SiO maser proper motions. These observations, taken as the Mira variable approached maximum light, show that over a 98-day period the masers have an average inward proper motion of ~1 mas. This contraction of the maser shell implies an infall velocity of ~4 km/s for the SiO masers during this phase of the stellar pulsation cycle. In addition to the total intensity images, maps of the linear and circular polarization morphology were also produced. These images show that the SiO masers are significantly polarized, and that the polarization structure and intensity change on timescales as short as ~1-2 months. For three of the four epochs, a mean fractional circular polarization of 4% was determined implying a magnetic field strength Bsec(theta) = 13 G. For one of the four epochs, the mean fractional circular polarization was found to be ~14% indicating a magnetic field strength Bsec(theta) = 46 G. The fractional linear polarization is fairly constant for all four epochs with mean values ranging from 20.8-25.0%, and peak values as high as ~83% for isolated maser features. Maps of the linear polarization vectors show an orderly structure over large portions of the maser shell indicating a uniform magnetic field topology in these regions of the extended atmosphere of R Aquarii. / Ph. D.