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Part-level representations are important for robust person re-identification (ReID), but in practice feature quality suffers due to the body part misalignment problem. In this paper, we present a robust, compact, and easy-to-use method called the Multi-task Part-aware Network (MPN), which is designed to extract semantically aligned part-level features from pedestrian images. MPN solves the body part misalignment problem via multi-task learning (MTL) in the training stage. More specifically, it builds one main task (MT) and one auxiliary task (AT) for each body part on the top of the same backbone model. The ATs are equipped with a coarse prior of the body part locations for training images. ATs then transfer the concept of the body parts to the MTs via optimizing the MT parameters to identify part-relevant channels from the backbone model. Concept transfer is accomplished by means of two novel alignment strategies: namely, parameter space alignment via hard parameter sharing and feature space alignment in a class-wise manner. With the aid of the learned high-quality parameters, MTs can independently extract semantically aligned part-level features from relevant channels in the testing stage. MPN has three key advantages: 1) it does not need to conduct body part detection in the inference stage; 2) its model is very compact and efficient for both training and testing; 3) in the training stage, it requires only coarse priors of body part locations, which are easy to obtain. Systematic experiments on four large-scale ReID databases demonstrate that MPN consistently outperforms state-of-the-art approaches by significant margins. Code is available at https://github.com/WangKan0128/MPN.