This chapter presents a mathematical approach to tackle the problem of localization of deformations in transformer windings. The approach essentially comprises of converting the measured driving-point impedance (via circuit synthesis) into a physically realizable, mutually coupled, ladder network that reproduces the measured characteristics as closely as possible. From a comparison of such synthesized circuits with the reference circuit, it is possible to assess the extent of damage the winding has undergone, in terms of the observed changes in the values of pertinent circuit elements. The task of localizing discrete changes was demonstrated using a model winding and an actual transformer winding. The localization accuracy achieved was reasonably good in all the experimental cases presented. Nevertheless, it is impossible to use this iterative technique to address the localization problem in practice. This is mainly because, the process is extremely slow when large-sized circuits have to be synthesized, as it employs a brute-force search strategy. This shortcoming was recognized and a far more superior and time-efficient alternative was suggested. One such idea, based on constrained-optimization technique was presented and discussed at the end of this chapter. The algorithm is still in the developmental stages and hence only preliminary results are reported. In spite of it, from the results presented it is clear that this method is highly time-efficient. It required only a few tens of seconds to synthesize a mutually coupled, 10-section ladder network. Therefore, it seems to be well suited to synthesize many such large-sized circuits rapidly, corresponding to each winding in a transformer. This feature makes it an ideal candidate for addressing the ultimate problem of localization of winding deformation in multi-winding transformers. In final summary, it is believed that with the suggested method, we are better equipped to address the problem of deformation localization in an actual multi-winding transformer.