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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 and theoretical physics, two geometries are conformally equivalent if there exists a conformal transformation (an angle-preserving transformation) that maps one geometry to the other one. More generally, two Riemannian metrics on a manifold M are conformally equivalent if one is obtained from the other by multiplication by a function on M. In mathematics, a conformal map is a function which preserves angles. In the most common case the function is between domains in the complex plane.