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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A differentiable manifold is a type of manifold that is locally similar enough to Euclidean space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since these lie in Euclidean spaces to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.