We study adversarially robust transfer learning, wherein, given labeled data on multiple (source) tasks, the goal is to train a model with small robust error on a previously unseen (target) task.In particular, we consider a multi-task representation learning (MTRL) setting, i.e., we assume that the source and target tasks admit a simple (linear) predictor on top of a shared representation (e.g., the final hidden layer of a deep neural network).In this general setting, we provide rates on~the excess adversarial (transfer) risk for Lipschitz losses and smooth nonnegative losses.These rates show that learning a representation using adversarial training on diverse tasks helps protect against inference-time attacks in data-scarce environments.Additionally, we provide novel rates for the single-task setting.