While multi-source adaptation has recently received much attention due to its effectiveness, limited effort has been made on improving its performance by leveraging some shared knowledge among sources and features. To this end, we propose in this paper a robust Multi-source co-Adaptation framework by mining diverse Correlation Information (MACI) among domains as well as features via joint adaptive $\sigma$-norm and correlation metric regularization. Concretely, multiple domain-invariant classification functions for different source adaptation objects are co-learned in a joint framework by minimizing both statistical and semantic distribution discrepancy between source and target domains, which enables MACI to utilize the correlated knowledge among multiple sources by exploiting the developed correlation metric function. Under this framework, MACI can preserve the original geometrical structure information as well as be robust to some noises or outliers existed in domains by employing local graph Laplacian and adaptive regression scheme. Furthermore, we also extend MACI to domain generalization scenario when the target domain of interest is unavailable in the training stage. An efficient iterative algorithm is proposed to optimize MACI (also applied to its domain generalization version), whose convergence is theoretically guaranteed. Comprehensive experimental evidence on a large number of visual datasets verifies the effectiveness of the proposed framework.