Title: Invariant Causal Representation Learning. Abstract: Due to spurious correlations, machine learning systems often fail to generalize to environments whose distributions differ from the ones used at training time. Prior work addressing this, either explicitly or implicitly, attempted to find a data representation that has an invariant causal relationship with the outcome. This is done by leveraging a diverse set of training environments to reduce the effect of spurious features, on top of which an invariant classifier is then built. However, these methods have generalization guarantees only when both data representation and classifiers come from a linear model class. As an alternative, we propose Invariant Causal Representation Learning (ICRL), a learning paradigm that enables out-of-distribution generalization in the nonlinear setting (i.e., nonlinear representations and nonlinear classifiers). It builds upon a practical and general assumption: data representations factorize when conditioning on the outcome and the environment. Based on this, we show identifiability up to a permutation and pointwise transformation. We also prove that all direct causes of the outcome can be fully discovered, which further enables us to obtain generalization guarantees in the nonlinear setting. Extensive experiments on both synthetic and real-world datasets show that our approach significantly outperforms a variety of baseline methods.