Breast Density Classification is a problem in Medical Imaging domain that aims to assign an American College of Radiology’s BIRADS category (I-IV) to a mammogram as an indication of tissue density. This is performed by radiologists in an qualitative way, and thus subject to variations from one physician to the other. In machine learning terms it is a 4-ordered-classes classification task with highly unbalance training data, as classes are not equally distributed among populations, even with variations among ethnicities. Deep Learning techniques in general became the state-of-the-art for many imaging classification tasks, however, dependent on the availability of large datasets. This is not often the case for Medical Imaging, and thus we explore Transfer Learning and Dataset Augmentationn. Results show a very high squared weighted kappa score of 0.81 (0.95 C.I. [0.77,0.85]) which is high in comparison to the 8 medical doctors that participated in the dataset labeling 0.82 (0.95 CI [0.77, 0.87]).