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Existing fully-supervised person re-identification (ReID) methods usually suffer from poor generalization capability caused by domain gaps. The key to solving this problem lies in filtering out identity-irrelevant interference and learning domain-invariant person representations. In this paper, we aim to design a generalizable person ReID framework which trains a model on source domains yet is able to generalize/perform well on target domains. To achieve this goal, we propose a simple yet effective Style Normalization and Restitution (SNR) module. Specifically, we filter out style variations (e.g., illumination, color contrast) by Instance Normalization (IN). However, such a process inevitably removes discriminative information. We propose to distill identity-relevant feature from the removed information and restitute it to the network to ensure high discrimination. For better disentanglement, we enforce a dual causal loss constraint in SNR to encourage the separation of identity-relevant features and identity-irrelevant features. Extensive experiments demonstrate the strong generalization capability of our framework. Our models empowered by the SNR modules significantly outperform the state-of-the-art domain generalization approaches on multiple widely-used person ReID benchmarks, and also show superiority on unsupervised domain adaptation.