According to the World Health Organization, breast cancer becomes fatal only if it spreads throughout the body. Therefore, regular screening is essential. Whilst mammography is the most frequently used technique, its interpretation can be challenging and time-consuming. For this reason, computer-aided detection and diagnosis systems are increasingly being used for second opinion. However, in order for doctors to trust such systems, they need to understand their decisions. We propose an automated and interpretable system for the detection and diagnosis of breast cancer, encompassing five steps. After a robust pre-processing and an unsupervised segmentation, we analyze four feature extraction techniques, both textural and shape-based, and three methods for feature selection. To facilitate interpretation, we employ the Decision Tree algorithm for benign/malignant classification and experiment with different methods to avoid overfitting: pre-pruning, post-pruning, and ensemble-based (Random Forest classifier). Our system reaches a maximum accuracy of 95% and 100% precision and specificity when tested on images from the mini-MIAS dataset, while also offering its users the possibility to analyze each of the steps.