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Most of existing methods for few-shot object detection follow the fine-tuning paradigm, which potentially assumes that the class-agnostic generalizable knowledge can be learned and transferred implicitly from base classes with abundant samples to novel classes with limited samples via such a two-stage training strategy. However, it is not necessarily true since the object detector can hardly distinguish between class-agnostic knowledge and class-specific knowledge automatically without explicit modeling. In this work we propose to learn three types of class-agnostic commonalities between base and novel classes explicitly: recognition-related semantic commonalities, localization-related semantic commonalities and distribution commonalities. We design a unified distillation framework based on a memory bank, which is able to perform distillation of all three types of commonalities jointly and efficiently. Extensive experiments demonstrate that our method can be readily integrated into most of existing fine-tuning based methods and consistently improve the performance by a large margin.