Differential machine learning combines automatic adjoin differentiation (AAD) with modern machine learning (ML) in the context of financial risk management. This work aims to resolve computational bottlenecks of derivatives risk reports and capital calculation by introducing novel algorithms for training fast, accurate pricing and risk approximation, online, in real time, with convergence guarantees. Differential ML is a general extension of supervised learning: the model is not only trained on examples of inputs and labels but also on differentials of labels with respect to inputs. It is also applicable in many situation outside finance, where high quality first-order derivatives with respect to training inputs are available.