Any account of Potential Theory now must ask of the inquirer a great deal more background knowledge. A good theory of integration, effectively incorporating both the Lebesgue and the Lebesgue-Stieltjes integral is essential, if only because one starts by working with semi-continuous functions and these need not be Riemann integrable at all. This and other requirements explain why, in this book, there is a considerable first chapter which sets out the background requirements for the rest of the book; and it is perhaps a mark of the change in the general level of mathematical sophistication over the period, that Kellogg was quite happy to set his theory in Euclidean three-dimensional space, but now one finds it necessary to start by setting up in business in a locally compact Hausdorff space!