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Many self-supervised learning (SSL) methods have been successful in learning semantically meaningful visual representations by solving pretext tasks. However, prior work in SSL focuses on tasks like object recognition or detection, which aim to learn object shapes and assume that the features should be invariant to concepts like colors and textures. Thus, these SSL methods perform poorly on downstream tasks where these concepts provide critical information. In this paper, we present an SSL framework that enables us to learn color and texture-aware features without requiring any labels during training. Our approach consists of three self-supervised tasks designed to capture different concepts that are neglected in prior work that we can select from depending on the needs of our downstream tasks. Our tasks include learning to predict color histograms and discriminate shapeless local patches and textures from each instance. We evaluate our approach on fashion compatibility using Polyvore Outfits and In-Shop Clothing Retrieval using Deepfashion, improving upon prior SSL methods by 9.5-16%, and even outperforming some supervised approaches on Polyvore Outfits despite using no labels. We also show that our approach can be used for transfer learning, demonstrating that we can train on one dataset while achieving high performance on a different dataset.