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This thesis deals with a novel approach for analyzing and computing interior transmission eigenvalues of (piecewise) homogeneous media in two dimensions. It is based on approximating boundary data of respective eigenfunctions by the method of fundamental solutions. However, since a straightforward implementation would solely exploit ill-conditioned matrices and thus evoke spurious results, a stabilization scheme is incorporated. The combined method is then studied with a distinction between isotropic and anisotropic materials, and complemented by novel approximation theory each. Numerical validations complete the investigations for different wave type scenarios