In this paper, we address the problem of multi-view clustering (MVC), integrating the close relationships among views to learn a consistent clustering result, via triplex information maximization (TIM). TIM works by proposing three essential principles, each of which is realized by a formulation of maximization of mutual information. 1) Principle 1: Contained. The first and foremost thing for MVC is to fully employ the self-contained information in each view. 2) Principle 2: Complementary. The feature-level complementary information across pairwise views should be first quantified and then integrated for improving clustering. 3) Principle 3: Compatible. The rich cluster-level shared compatible information among individual clustering of each view is significant for ensuring a better final consistent result. Following these principles, TIM can enjoy the best of view-specific, cross-view feature-level, and cross-view cluster-level information within/among views. For principle 2, we design an automatic view correlation learning (AVCL) mechanism to quantify how much complementary information across views by learning the cross-view weights between pairwise views automatically, instead of view-specific weights as most existing MVCs do. Specifically, we propose two different strategies for AVCL, i.e., feature-based and cluster-based strategy, for effective cross-view weight learning, thus leading to two versions of our method, TIM-F and TIM-C, respectively. We further present a two-stage method for optimization of the proposed methods, followed by the theoretical convergence and complexity analysis. Extensive experimental results suggest the effectiveness and superiority of our methods over many state-of-the-art methods.