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This classic work is now available in an unabridged paperback edition. Stoker makes this fertile branch of mathematics accessible to the no specialist by the use of three different notations: vector algebra and calculus, tensor calculus and the notation devised by Cartan, which employs invariant differential forms as elements in algebra due to Grass man, combined with an operation called exterior differentiation. Assumed are a passing acquaintance with linear algebra and the basic elements of analysis.