We are interested in the ethical aspects of algorithmic decision-making and learning according to the principles of Fairness, Accountability, Transparency and Explainablity (FATE). Our goal is to determine the algorithms' properties with regards to these principles as this will allow for better understanding of their impact. We aim to achieve this by (i) improving the explainability of decisions by leveraging their mathematical properties, (ii) identifying metrics of fairness and providing certificates of fairness for these metrics, and (iii) presenting efficient algorithms for identifying these solutions.