Algorithmic Fairness is an established area of machine learning, willing to reduce the influence of biases in the data. Yet, despite its wide range of applications, very few works consider the multi-class classification setting from the fairness perspective. In this talk, we consider the multi-class classification framework and focus on the demographic parity notion of fairness. We exhibit algorithms that can adapt to a desired pre-specified level of fairness, that is, we consider both exact and approximate fairness problems. We illustrate the performance of these algorithms in terms of risk and fairness through finite sample bounds and numerical results.