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Contemporary monocular 6D pose estimation methods can only cope with a handful of object instances. This naturally hampers possible applications as, for instance, robots seamlessly integrated in everyday processes necessarily require the ability to work with hundreds of different objects. To tackle this problem of immanent practical relevance, we propose a novel method for class-level monocular 6D pose estimation, coupled with metric shape retrieval. Unfortunately, acquiring adequate annotations is very time-consuming and labor intensive. This is especially true for class-level 6D pose estimation, as one is required to create a highly detailed reconstruction for all objects and then annotate each object and scene using these models. To overcome this shortcoming, we additionally propose the idea of synthetic-to-real domain transfer for class-level 6D poses by means of self-supervised learning, which removes the burden of collecting numerous manual annotations. In essence, after training our proposed method fully supervised with synthetic data, we leverage recent advances in differentiable rendering to self-supervise the model with unannotated real RGB-D data to improve latter inference. We experimentally demonstrate that we can retrieve precise 6D poses and metric shapes from a single RGB image.