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We present a self-supervised algorithm for several classification tasks within hematoxylin and eosin (H&E) stained images of breast cancer. Our method is robust to stain variations inherent to the histology images acquisition process, which has limited the applicability of automated analysis tools. We address this problem by imposing constraints a learnt latent space which leverages stain normalization techniques during training. At every iteration, we select an image as a normalization target and generate a version of every image in the batch normalized to that target. We minimize the distance between the embeddings that correspond to the same image under different staining variations while maximizing the distance between other samples. We show that our method not only improves robustness to stain variations across multi-center data, but also classification performance through extensive experiments on various normalization targets and methods. Our method achieves the state-of-the-art performance on several publicly available breast cancer datasets ranging from tumor classification (CAMELYON17) and subtyping (BRACS) to HER2 status classification and treatment response prediction.