51-XX	Geometry {For algebraic geometry, see 14-XX}
51-00	General reference works (handbooks, dictionaries, bibliographies, etc.)
51-01	Instructional exposition (textbooks, tutorial papers, etc.)
51-02	Research exposition (monographs, survey articles)
51-03	Historical {!must also be assigned at least one classification number from section 01}
51-04	Explicit machine computation and programs (not the theory of computation or programming)
51-06	Proceedings, conferences, collections, etc.
51Axx	Linear incidence geometry
51A05	General theory and projective geometries
51A10	Homomorphism, automorphism and dualities
51A15	Structures with parallelism
51A20	Configuration theorems
51A25	Algebraization [See also 12Kxx, 20N05]
51A30	Desarguesian and Pappian geometries
51A35	Non-Desarguesian affine and projective planes
51A40	Translation planes and spreads
51A45	Incidence structures imbeddable into projective geometries
51A50	Polar geometry, symplectic spaces, orthogonal spaces
51A99	None of the above, but in this section
51Bxx	Nonlinear incidence geometry
51B05	General theory
51B10	M\"obius geometries
51B15	Laguerre geometries
51B20	Minkowski geometries
51B25	Lie geometries
51B99	None of the above, but in this section
51C05	Ring geometry (Hjelmslev, Barbilian, etc.)
51Dxx	Geometric closure systems
51D05	Abstract (Maeda) geometries
51D10	Abstract geometries with exchange axiom
51D15	Abstract geometries with parallelism
51D20	Combinatorial geometries [See also 05B25, 05B35]
51D25	Lattices of subspaces [See also 05B35]
51D30	Continuous geometries and related topics [See also 06Cxx]
51D99	None of the above, but in this section
51Exx	Finite geometry and special incidence structures
51E05	General block designs [See also 05B05]
51E10	Steiner systems
51E12	Generalized quadrangles, generalized polygons
51E14	Finite partial geometries (general), nets, partial spreads
51E15	Affine and projective planes
51E20	Combinatorial structures in finite projective spaces [See also 05Bxx]
51E21	Blocking sets, ovals, k-arcs
51E22	Linear codes and caps in Galois spaces [See also 94B05]
51E23	Spreads and packing problems
51E24	Buildings and the geometry of diagrams
51E25	Other finite nonlinear geometries
51E26	Other finite linear geometries
51E30	Other finite incidence structures [See also 05B30]
51E99	None of the above, but in this section
51Fxx	Metric geometry
51F05	Absolute planes
51F10	Absolute spaces
51F15	Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55]
51F20	Congruence and orthogonality [See also 20H05]
51F25	Orthogonal and unitary groups [See also 20H05]
51F99	None of the above, but in this section
51G05	Ordered geometries (ordered incidence structures, etc.)
51Hxx	Topological geometry
51H05	General theory
51H10	Topological linear incidence structures
51H15	Topological nonlinear incidence structures
51H20	Topological geometries on manifolds [See also 57-XX]
51H25	Geometries with differentiable structure [See also 53Cxx, 53C70]
51H30	Geometries with algebraic manifold structure [See also 14-XX]
51H99	None of the above, but in this section
51Jxx	Incidence groups
51J05	General theory
51J10	Projective incidence groups
51J15	Kinematic spaces
51J20	Representation by near-fields and near-algebras [See also 12K05, 16Y30]
51J99	None of the above, but in this section
51Kxx	Distance geometry
51K05	General theory
51K10	Synthetic differential geometry
51K99	None of the above, but in this section
51Lxx	Geometric order structures [See also 53C75]
51L05	Geometry of orders of nondifferentiable curves
51L10	Directly differentiable curves
51L15	n-vertex theorems via direct methods
51L20	Geometry of orders of surfaces
51L99	None of the above, but in this section
51Mxx	Real and complex geometry
51M04	Elementary problems in Euclidean geometries
51M05	Euclidean geometries (general) and generalizations
51M09	Elementary problems in hyperbolic and elliptic geometries
51M10	Hyperbolic and elliptic geometries (general) and generalizations
51M15	Geometric constructions
51M16	Inequalities and extremum problems {For convex problems, see 52A40}
51M20	Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]
51M25	Length, area and volume [See also 26B15]
51M30	Line geometries and their generalizations [See also 53A25]
51M35	Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) [See also 14M15]
51M99	None of the above, but in this section
51Nxx	Analytic and descriptive geometry
51N05	Descriptive geometry [See also 65D17, 68U07]
51N10	Affine analytic geometry
51N15	Projective analytic geometry
51N20	Euclidean analytic geometry
51N25	Analytic geometry with other transformation groups
51N30	Geometry of classical groups [See also 20Gxx, 14L35]
51N35	Questions of classical algebraic geometry [See also 14Nxx]
51N99	None of the above, but in this section
51P05	Geometry and physics {!should also be assigned at least one other classification number from sections 70-86}