Bi-KVIL is a keypoints-based visual imitation learning approach for bimanual manipulation tasks. It extends the previous work on K-VIL to handle bimanual coordination strategies and complex object relations. The method jointly extracts Hybrid Master-Slave Relationships (HMSR) among objects and hands, bimanual coordination strategies, and sub-symbolic task representations. The bimanual task representation is object-centric, embodiment-independent, and viewpoint-invariant, enabling generalization to categorical objects in novel scenes. Bi-KVIL automatically extracts HMSR, bimanual coordination strategies, and sub-symbolic task representations, including keypoints-based geometric constraints on principal manifolds, their associated local frames, and movement primitives. It also introduces a bimanual keypoint-based admittance controller (Bi-KAC) to handle prioritized geometric constraints for bimanual tasks. Bi-KVIL is evaluated on various real-world tasks, demonstrating its ability to learn fine-grained bimanual manipulation tasks from a small number of human demonstration videos. The method outperforms data-driven approaches in terms of the number of demonstrations and category-level generalization. Bi-KVIL is the first to simultaneously extract bimanual coordination strategies and generalizable geometric task constraints from few visual demonstrations. The approach is robust to object (self-)occlusion and provides high-quality datasets for visual imitation learning. However, it may fail in bimanual transport tasks due to the lack of dual-arm synchronization. Future work aims to address these limitations and investigate a comprehensive evaluation benchmark for bimanual imitation learning tasks.Bi-KVIL is a keypoints-based visual imitation learning approach for bimanual manipulation tasks. It extends the previous work on K-VIL to handle bimanual coordination strategies and complex object relations. The method jointly extracts Hybrid Master-Slave Relationships (HMSR) among objects and hands, bimanual coordination strategies, and sub-symbolic task representations. The bimanual task representation is object-centric, embodiment-independent, and viewpoint-invariant, enabling generalization to categorical objects in novel scenes. Bi-KVIL automatically extracts HMSR, bimanual coordination strategies, and sub-symbolic task representations, including keypoints-based geometric constraints on principal manifolds, their associated local frames, and movement primitives. It also introduces a bimanual keypoint-based admittance controller (Bi-KAC) to handle prioritized geometric constraints for bimanual tasks. Bi-KVIL is evaluated on various real-world tasks, demonstrating its ability to learn fine-grained bimanual manipulation tasks from a small number of human demonstration videos. The method outperforms data-driven approaches in terms of the number of demonstrations and category-level generalization. Bi-KVIL is the first to simultaneously extract bimanual coordination strategies and generalizable geometric task constraints from few visual demonstrations. The approach is robust to object (self-)occlusion and provides high-quality datasets for visual imitation learning. However, it may fail in bimanual transport tasks due to the lack of dual-arm synchronization. Future work aims to address these limitations and investigate a comprehensive evaluation benchmark for bimanual imitation learning tasks.