The astonishing diversity in folding patterns of RNA three-dimensional (3D) structures is crafted by myriads of noncovalent contacts, of which base pairing and stacking are the most prominent. A systematic and comprehensive classification and annotation of these interactions is necessary for a molecular-level understanding of their roles. However, unlike in the case of base pairing, where a widely accepted nomenclature and classification scheme exists in the public domain, currently available classification schemes for base-base stacking need major enhancements to comprehensively capture the necessary features underlying the rich stacking diversity in RNA. Here, we extend the previous stacking classification based on nucleobase interacting faces by introducing a structurally intuitive geometry-cum topology-based scheme. Specifically, a stack is first classified in terms of the geometry described by the relative orientation of the glycosidic bonds, which generates eight basic stacking geometric families for heterodimeric stacks and six of those for homodimeric stacks. Further annotation in terms of the identity of the bases and the region of involvement of purines (five-membered, six-membered, or both rings) leads to the enumeration of 384 distinct RNA base stacks. Based on our classification scheme, we present an algorithm for automated identification of stacks in RNA crystal structures and analyze the stacking context in selected RNA structures. Overall, the work described here is expected to greatly facilitate the structure-based RNA research.