This paper presents a novel transformation-proximal bundle algorithm to solve multistage adaptive robust mixed-integer linear programs (MARMILPs). By explicitly partitioning recourse decisions into state decisions and local decisions, the proposed algorithm applies affine decision rule only to state decisions and allows local decisions to be fully adaptive. In this way, the MARMILP is proved to be transformed into an equivalent two-stage adaptive robust optimization (ARO) problem. The proposed multi-to-two transformation scheme remains valid for other types of non-anticipative decision rules besides the affine one, and it is general enough to be employed with existing two-stage ARO algorithms for solving MARMILPs. The proximal bundle method is developed for the resulting two-stage ARO problem. We perform a theoretical analysis to show finite convergence of the proposed algorithm with any positive tolerance. To quantitatively assess solution quality, we develop a scenario-tree-based lower bounding technique. Computational studies on multiperiod inventory management and process network planning are presented to demonstrate its effectiveness and computational scalability. In the inventory management application, the affine decision rule method suffers from a severe suboptimality with an average gap of 34.88%, while the proposed algorithm generates near-optimal solutions with an average gap of merely 1.68%. contingency plans beforehand, and picks a best one among these preselected plans after knowing uncertainty realizations (Bertsimas and Caramanis 2010). Despite its intuitive convenience, the resulting K-adaptability problem usually provides a suboptimal solution (Hanasusanto et al. 2015). Moreover, it is computationally challenging to extend the concept of K-adaptability to ARO problems with multiple time stages. The reason is that the number of required contingency plans grows exponentially with the number of stages. Reformulation-approximation methods, including a copositive approach and linearized robust counterpart, conservatively express two-stage ARO problem as a single-level optimization problem, which is then amenable for off-the-shelf optimization solvers (Ardestani-Jaafari and Delage 2016, Xu and Burer 2018). In addition to the above conservative approximation solution methods, the Benders decomposition method and the extreme point enumeration approach were proposed as exact solution techniques exclusively suitable for two-stage ARO problems (Takeda et al. 2008, Thiele et al. 2009, Zeng and Zhao 2013. Recently, a primal-dual lifting scheme was proposed to solve two-stage ARO problems by integrating affine decision rule with enumeration of extreme points in a hybrid way (Georghiou et al. 2017).Despite the broad application scope of the multistage setting, solution techniques for multistage ARO problems are very limited based on the existing literature, and they usually suffer from an unsatisfactory trade-off between solution quality and computational tractability. Hence, the research objective of our work...