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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-Shnirelman) category of a space
55M35 Finite groups of transformations (including Smith theory) [See also 57S17]
55M99 None of the above, but in this section