Key to effective person re-identification (Re-ID) is modelling discriminative and view-invariant factors of person appearance at both high and low semantic levels. Recently developed deep Re-ID models either learn a holistic single semantic level feature representation and/or require laborious human annotation of these factors as attributes. We propose Multi-Level Factorisation Net (MLFN), a novel network architecture that factorises the visual appearance of a person into latent discriminative factors at multiple semantic levels without manual annotation. MLFN is composed of multiple stacked blocks. Each block contains multiple factor modules to model latent factors at a specific level, and factor selection modules that dynamically select the factor modules to interpret the content of each input image. The outputs of the factor selection modules also provide a compact latent factor descriptor that is complementary to the conventional deeply learned features. MLFN achieves state-of-the-art results on three Re-ID datasets, as well as compelling results on the general object categorisation CIFAR-100 dataset.