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In this paper, we look into the problem of estimating per-pixel depth maps from unconstrained RGB monocular night-time images which is a difficult task that has not been addressed adequately in the literature. The state-of-the-art day-time depth estimation methods fail miserably when tested with night-time images due to a large domain shift between them. The usual photo metric losses used for training these networks may not work for night-time images due to the absence of uniform lighting which is commonly present in day-time images, making it a difficult problem to solve. We propose to solve this problem by posing it as a domain adaptation problem where a network trained with day-time images is adapted to work for night-time images. Specifically, an encoder is trained to generate features from night-time images that are indistinguishable from those obtained from day-time images by using a PatchGAN-based adversarial discriminative learning method. Unlike the existing methods that directly adapt depth prediction (network output), we propose to adapt feature maps obtained from the encoder network so that a pre-trained day-time depth decoder can be directly used for predicting depth from these adapted features. Hence, the resulting method is termed as "Adversarial Domain Feature Adaptation (ADFA)" and its efficacy is demonstrated through experimentation on the challenging Oxford night driving dataset. Also, The modular encoder-decoder architecture for the proposed ADFA method allows us to use the encoder module as a feature extractor which can be used in many other applications. One such application is demonstrated where the features obtained from our adapted encoder network are shown to outperform other state-of-the-art methods in a visual place recognition problem, thereby, further establishing the usefulness and effectiveness of the proposed approach.