Knowledge distillation (KD), as an efficient and effective model compression technique, has been receiving considerable attention in deep learning. The key to its success is to transfer knowledge from a large teacher network to a small student one. However, most of the existing knowledge distillation methods consider only one type of knowledge learned from either instance features or instance relations via a specific distillation strategy in teacher-student learning. There are few works that explore the idea of transferring different types of knowledge with different distillation strategies in a unified framework. Moreover, the frequently used offline distillation suffers from a limited learning capacity due to the fixed teacher-student architecture. In this paper we propose a collaborative teacher-student learning via multiple knowledge transfer (CTSL-MKT) that prompts both self-learning and collaborative learning. It allows multiple students learn knowledge from both individual instances and instance relations in a collaborative way. While learning from themselves with self-distillation, they can also guide each other via online distillation. The experiments and ablation studies on four image datasets demonstrate that the proposed CTSL-MKT significantly outperforms the state-of-the-art KD methods.