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We provide a summary of the continuity properties of the boundary integraloperator corresponding to the double layer potential associated to thefundamental solution of a {\em nonhomogeneous} second order ellipticdifferential operator with constant coefficients in H\"{o}lder and Schauderspaces on the boundary of a bounded open subset of ${\mathbb{R}}^n$.  The purpose is two-fold. On one hand we try present in a single paper all theknown continuity results on the topic with the best known exponents in aH\"{o}lder and Schauder space setting and on the other hand we show that manyof the properties we present can be deduced by applying results that hold in anabstract setting of metric spaces with a measure that satisfies certain growthconditions that include non-doubling measures as in a series of papers byGarc\'{\i}a-Cuerva and Gatto in the frame of H\"{o}lder spaces and later by theauthor.

A survey on the boundary behavior of the double layer potential in Schauder spaces in the frame of an abstract approach