Segmentation of mammograms pertains to assigning a meaningful label to each pixel found in the image. The segmented mammogram facilitates both the function of Computer Aided Diagnosis Systems and the development of tools used by radiologists during examination. Over the years many approaches to this problem have been presented. A surge in the popularity of new methods to image processing involving deep neural networks present new possibilities in this domain, and this thesis evaluates mammogram segmentation as an application of a specialized neural network architecture, U-net. Results are produced on publicly available datasets mini-MIAS and CBIS-DDSM. Using these two datasets together with mammograms from Hologic and FUJI, instances of U-net are trained and evaluated within and across the different datasets. A total of 10 experiments are conducted using 4 different models. Averaged over classes Pectoral, Breast and Background the best Dice scores are: 0.987 for Hologic, 0.978 for FUJI, 0.967 for mini-MIAS and 0.971 for CBIS-DDSM.