This thesis is in the area of ultrasound tomography, which is a non-destructive imaging method that attempts to create quantitative images of the acoustical properties of an object of interest (OI). Specifically, three quantitative images per OI are created in this thesis, two of which correspond to the complex compressibility profile of the OI, and the other corresponds to its density profile. The focus of this thesis is on the development of an appropriate two-dimensional inverse scattering algorithm to create these quantitative images. The core of this algorithm is the Born iterative method that is used in conjunction with a fast and efficient method of moments forward solver, a Krylov subspace regularization technique, and a balancing method. This inversion algorithm is capable of simultaneous inversion of multiple-frequency data, and can handle a large imaging domain. This algorithm is finally tested against synthetic and measured data.

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