Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain.Formally, classifying manifolds is classifying objects up to isomorphism. There are many different notions of "manifold", and corresponding notions of "map between manifolds", each of which yields a different category and a different classification question.Many of these structures are G-structures, and the question is reduction of the structure group. The most familiar example is orientability: some manifolds are orientable, some are not, and orientable manifolds admit 2 orientations.

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