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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, a volume form on a differentiable manifold is a nowhere vanishing differential form of top degree. A volume form provides a means to define the integral of a function on a differentiable manifold. In other words, a volume form gives rise to a measure with respect to which functions can be integrated by the appropriate Lebesgue integral. The absolute value of a volume form is a volume element, which is also known variously as a twisted volume form or pseudo-volume form. It also defines a measure, but exists on any differentiable manifold, orientable or not.