The paper involves the distributed robust adaptive learning coordination control for high-order nonlinear multi-agent systems, where the leader has nonzero Small Mug input and followers are subject to input saturation.To solve the problem, two initial assumptions concerning initial state learning and alignment initial condition are introduced, and the distributed learning protocols as well as parameter adaptive laws are designed.It should be noted that the protocols proposed under initial state learning containing the global information are not fully distributed, while the fully distributed protocols can be obtained by the alignment initial condition.Through the rigorous analysis, it is proved that each follower can perfectly track the leader on a finite time Shampoos interval under both two assumptions.Then, the consensus results under the alignment initial condition are generalized to formation control and two simulation examples verify the correctness and feasibility of the proposed algorithms.