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Monocular depth estimation (MDE) has attracted intense study due to its low cost and critical functions for robotic tasks such as localization, mapping and obstacle detection. Supervised approaches have led to great success with the advance of deep learning, but they rely on large quantities of ground-truth depth annotations that are expensive to acquire. Unsupervised domain adaptation (UDA) transfers knowledge from labeled source data to unlabeled target data, so as to relax the constraint of supervised learning. However, existing UDA approaches may not completely align the domain gap across different datasets because of the domain shift problem. We believe better domain alignment can be achieved via well-designed feature decomposition. In this paper, we propose a novel UDA method for MDE, referred to as Learning Feature Decomposition for Adaptation (LFDA), which learns to decompose the feature space into content and style components. LFDA only attempts to align the content component since it has a smaller domain gap. Meanwhile, it excludes the style component which is specific to the source domain from training the primary task. Furthermore, LFDA uses separate feature distribution estimations to further bridge the domain gap. Extensive experiments on three domain adaptative MDE scenarios show that the proposed method achieves superior accuracy and lower computational cost compared to the state-of-the-art approaches.