55-XX	Algebraic topology
55-00	General reference works (handbooks, dictionaries, bibliographies, etc.)
55-01	Instructional exposition (textbooks, tutorial papers, etc.)
55-02	Research exposition (monographs, survey articles)
55-03	Historical {!must also be assigned at least one classification number from section 01}
55-04	Explicit machine computation and programs (not the theory of computation or programming)
55-06	Proceedings, conferences, collections, etc.
55Mxx	Classical topics {For the topology of Euclidean spaces and manifolds, see 57Nxx}
55M05	Duality
55M10	Dimension theory [See also 54F45]
55M15	Absolute neighborhood retracts [See also 54C55]
55M20	Fixed points and coincidences [See also 54H25]
55M25	Degree, winding number
55M30	Ljusternik - Schnirelman (Lyusternik - Shnirel'man) category of a space
55M35	Finite groups of transformations (including Smith theory) [See also 57S17]
55M99	None of the above, but in this section
55Nxx	Homology and cohomology theories [See also 57Txx]
55N05	Cech types
55N07	Steenrod - Sitnikov homologies
55N10	Singular theory
55N15	K-theory [See also 19Lxx] {For algebraic K-theory, see 18F25, 19-XX}
55N20	Generalized (extraordinary) homology and cohomology theories
55N22	Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]
55N25	Homology with local coefficients, equivariant cohomology
55N30	Sheaf cohomology [See also 18F20, 32C35, 32L10]
55N33	Intersection homology and cohomology
55N34	Elliptic cohomology
55N35	Other homology theories
55N40	Axioms for homology theory and uniqueness theorems
55N45	Products and intersections
55N91	Equivariant homology and cohomology [See also 19L47]
55N99	None of the above, but in this section
55Pxx	Homotopy theory {For simple homotopy type, see 57Q10}
55P05	Homotopy extension properties, cofibrations
55P10	Homotopy equivalences
55P15	Classification of homotopy type
55P20	Eilenberg - Mac_Lane spaces
55P25	Spanier - Whitehead duality
55P30	Eckmann - Hilton duality
55P35	Loop spaces
55P40	Suspensions
55P42	Stable homotopy theory, spectra
55P43	Spectra with additional structure (Einfty, Ainfty, ring spectra, etc.)
55P45	H-spaces and duals
55P47	Infinite loop spaces
55P48	Loop space machines, operads [See also 18D50]
55P50	Category and cocategory, etc.
55P55	Shape theory [See also 54C56, 55Q07]
55P57	Proper homotopy theory
55P60	Localization and completion
55P62	Rational homotopy theory
55P65	Homotopy functors
55P91	Equivariant homotopy theory [See also 19L47]
55P92	Relations between equivariant and nonequivariant homotopy theory
55P99	None of the above, but in this section
55Qxx	Homotopy groups
55Q05	Homotopy groups, general; sets of homotopy classes
55Q07	Shape groups
55Q10	Stable homotopy groups
55Q15	Whitehead products and generalizations
55Q20	Homotopy groups of wedges, joins, and simple spaces
55Q25	Hopf invariants
55Q35	Operations in homotopy groups
55Q40	Homotopy groups of spheres
55Q45	Stable homotopy of spheres
55Q50	J-morphism [See also 19L20]
55Q51	Vn-periodicity
55Q52	Homotopy groups of special spaces
55Q55	Cohomotopy groups
55Q70	Homotopy groups of special types [See also 55N05, 55N07]
55Q91	Equivariant homotopy groups [See also 19L47]
55Q99	None of the above, but in this section
55Rxx	Fiber spaces and bundles [See also 18F15, 32Lxx, 46M20, 57R20, 57R22, 57R25]
55R05	Fiber spaces
55R10	Fiber bundles
55R12	Transfer
55R15	Classification
55R20	Spectral sequences and homology of fiber spaces [See also 55Txx]
55R25	Sphere bundles and vector bundles
55R35	Classifying spaces of groups and H-spaces
55R37	Maps between classifying spaces
55R40	Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
55R45	Homology and homotopy of B\rmO and B\rmU; Bott periodicity
55R50	Stable classes of vector space bundles, K-theory [See also 19Lxx] {For algebraic K-theory, see 18F25, 19-XX}
55R55	Fiberings with singularities
55R60	Microbundles and block bundles [See also 57N55, 57Q50]
55R65	Generalizations of fiber spaces and bundles
55R70	Fibrewise topology
55R80	Discriminantal varieties, configuration spaces
55R91	Equivariant fiber spaces and bundles [See also 19L47]
55R99	None of the above, but in this section
55Sxx	Operations and obstructions
55S05	Primary cohomology operations
55S10	Steenrod algebra
55S12	Dyer - Lashof operations
55S15	Symmetric products, cyclic products
55S20	Secondary and higher cohomology operations
55S25	K-theory operations and generalized cohomology operations [See also 19D55, 19Lxx]
55S30	Massey products
55S35	Obstruction theory
55S36	Extension and compression of mappings
55S37	Classification of mappings
55S40	Sectioning fiber spaces and bundles
55S45	Postnikov systems, k-invariants
55S91	Equivariant operations and obstructions [See also 19L47]
55S99	None of the above, but in this section
55Txx	Spectral sequences [See also 18G40, 55R20]
55T05	General
55T10	Serre spectral sequences
55T15	Adams spectral sequences
55T20	Eilenberg - Moore spectral sequences [See also 57T35]
55T25	Generalized cohomology
55T99	None of the above, but in this section
55Uxx	Applied homological algebra and category theory [See also 18Gxx]
55U05	Abstract complexes
55U10	Semisimplicial complexes
55U15	Chain complexes
55U20	Universal coefficient theorems, Bockstein operator
55U25	Homology of a product, K\"unneth formula
55U30	Duality
55U35	Abstract and axiomatic homotopy theory
55U40	Topological categories, foundations of homotopy theory
55U99	None of the above, but in this section