Abstract: Over the last decade, there has been tremendous progress in classifying and identifying material realizations of topological (crystalline) insulators (TIs and TCIs) by leveraging the group theory of crystalline solids. Most recently, our team performed the first complete classification of and high-throughput search for magnetically ordered topological materials using the symmetries of the magnetic space groups (MSGs) [1,2]. Along a parallel track, researchers for the past 20 years have poured enormous effort into better understanding and predicting topological superconductors (TSCs). Though there have been incipient recent efforts to classify TSCs with crystal symmetries and perform large-scale material searches, these studies have largely been limited to weak-coupling superconductors (SCs) and SCs with unconventional pairing symmetries, for which definitive material realizations are rare. In this talk, I will present a new, real-space theory of crystalline TSCs that functions in the strong-pairing regime and is fully agnostic as to the SC pairing symmetry. Our approach is instead facilitated by introducing a refined notion of SC space groups (SC-SGs) analogous to the MSGs. Using the SC-SGs, we then introduce model-independent topological diagnosis schemes for TSCs with and without time-reversal symmetry through a new framework of U(1) charge-resolved topology, which can viewed as “dual” to the U(1) spin-resolved crystalline topology recently introduced by our team to unravel the bulk responses of TCIs [3]. Our analysis reveals new hierarchical structures of TSCs and relationships between normal-state topological phases and crystalline TSCs, whose surface theories expand upon and recontextualize the celebrated Fu-Kane proximity effect.