This book may be considered as logical continuation of the previously published (V.I. Fabrikant, Applications of Potential Theory in Mechanics, Kluwer Academic, 1989), where a new and elementary method was described for solving mixed boundary value problems. The method can solve non-axisymmetric problems as easily as axisymmetric ones, exactly and in closed form. It enables us to treat analytically non-classical domains. The method also provides, as a bonus, a tool for exact evaluation of various two-dimensional integrals involving distances between two or more points.