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While autonomous vehicles still struggle to solve challenging situations during on-road driving, humans have long mastered the essence of driving with efficient, transferable, and adaptable driving capability. By mimicking humans' cognition model and semantic understanding during driving, we propose HATN, a hierarchical framework to generate high-quality, transferable, and adaptable predictions for driving behaviors in multi-agent dense-traffic environments. Our hierarchical method consists of a high-level intention identification policy and a low-level trajectory generation policy. We introduce a novel semantic sub-task definition and generic state representation for each sub-task. With these techniques, the hierarchical framework is transferable across different driving scenarios. Besides, our model is able to capture variations of driving behaviors among individuals and scenarios by an online adaptation module. We demonstrate our algorithms in the task of trajectory prediction for real traffic data at intersections and roundabouts from the INTERACTION dataset. Through extensive numerical studies, it is evident that our method significantly outperformed other methods in terms of prediction accuracy, transferability, and adaptability. Pushing the state-of-the-art performance by a considerable margin, we also provide a cognitive view of understanding the driving behavior behind such improvement. We highlight that in the future, more research attention and effort are deserved for transferability and adaptability. It is not only due to the promising performance elevation of prediction and planning algorithms, but more fundamentally, they are crucial for the scalable and general deployment of autonomous vehicles.