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"Regularity theory" as a book category would gather works concerned with the emergence, characterization and proof of smoothness, structure, and stability in mathematical and applied problems. Primarily rooted in analysis and partial differential equations, it would include textbooks, graduate monographs, lecture notes and research surveys on topics such as elliptic and parabolic regularity, Schauder and Calderón–Zygmund estimates, De Giorgi–Nash–Moser theory, geometric measure theory, and regularity for variational problems and free boundaries. Collections in this category would span rigorous proofs and techniques, worked examples and counterexamples, and applications to fluid mechanics, materials science, geometry and applied modelling; they would be aimed at advanced undergraduates, graduate students and researchers. Broadly construed, the label could also encompass interdisciplinary treatments of regularity and pattern formation in dynamical systems, statistics and data science, or accessible expositions about how order and smoothness arise in natural and engineered systems.

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