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In this paper, we propose and analyze a novel shape reconstruction technique for the early detection of breast cancer from microwave data, which is based on a level-set technique. The shape-based approach offers several advantages compared to more traditional pixel-based approaches when targeting the reconstruction of key characteristics of a hidden tumor such as its correct size, shape, and static permittivity value. In addition to these key characteristics of hidden tumors, we aim at estimating the correct interfaces between fatty and fibroglandular tissue in the breast and their internal permittivity profiles. The level set strategy (which is an implicit representation of the shapes) frees us from topological restrictions when reconstructing an a priori arbitrary number of tumors and the often quite complicated interfaces between fatty and fibroglandular regions. The presented strategy is able to detect and, in most cases, characterize tumors whose sizes (diameters) are much smaller than the wavelengths of the electromagnetic waves that are used for illuminating the breast. We present numerical results for a 2-D model with two distinct tissue types (fatty and fibroglandular) in the interior of the breast (in addition to a possible tumor and the surrounding skin). Our results demonstrate the performance and potential of our scheme in various simulated but realistic situations.