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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, contact geometry is the study of a geometric structure on smooth manifolds given by a hyperplane distribution in the tangent bundle and specified by a one-form, both of which satisfy a ''maximum non-degeneracy'' condition called ''complete non-integrability''. From the Frobenius theorem, one recognizes the condition as the opposite of the condition that the distribution be determined by a codimension one foliation on the manifold (''complete integrability'').