Abstract: A major drawback of adversarially robust models, in particular for large scale datasets like ImageNet, is the extremely long training time compared to standard models. Moreover, models should be robust not only to one $l_p$-threat model but ideally to all of them. In this paper we propose Extreme norm Adversarial Training (E-AT) for multiple-norm robustness which is based on geometric properties of $l_p$-balls. E-AT costs up to three times less than other adversarial training methods for multiple-norm robustness. Using E-AT we show that for ImageNet a single epoch and for CIFAR-10 three epochs are sufficient to turn any $l_p$-robust model into a multiple-norm robust model. In this way we get the first multiple-norm robust model for ImageNet and boost the state-of-the-art for multiple-norm robustness to more than $51\%$ on CIFAR-10. Finally, we study the general transfer via fine-tuning of adversarial robustness between different individual $l_p$-threat models and improve the previous SOTA $l_1$-robustness on both CIFAR-10 and ImageNet. Extensive experiments show that our scheme works across datasets and architectures including vision transformers.