| 51-00 | General reference works (handbooks, dictionaries, bibliographies, etc.)
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| 51-01 | Instructional exposition (textbooks, tutorial papers, etc.)
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| 51-02 | Research exposition (monographs, survey articles)
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| 51-03 | Historical (must also be assigned at least one classification number from Section 01)
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| 51-04 | Explicit machine computation and programs (not the theory of computation or programming)
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| 51-06 | Proceedings, conferences, collections, etc.
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| 51Axx | Linear incidence geometry
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| 51Bxx | Nonlinear incidence geometry
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| 51C05 | Ring geometry (Hjelmslev, Barbilian, etc.)
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| 51Dxx | Geometric closure systems
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| 51Exx | Finite geometry and special incidence structures
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| 51Fxx | Metric geometry
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| 51G05 | Ordered geometries (ordered incidence structures, etc.)
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| 51Hxx | Topological geometry
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| 51Jxx | Incidence groups
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| 51Kxx | Distance geometry
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| 51Lxx | Geometric order structures [See also 53C75]
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| 51Mxx | Real and complex geometry
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| 51Nxx | Analytic and descriptive geometry
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| 51P05 | Geometry and physics (should also be assigned at least one other classification number from Sections 70--86)
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