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This book addresses largely three-dimensional problems. Scattering problems for bodies, small in comparison with the wavelength, are reduced to static problems. Complex variable methods (conformal mappings) for solving static two-dimensional problems have been widely discussed in the literature. The problems solvable in closed form are collected in [13], [33], [43], [58], [143], [71], [73]. The method of separation of variables has been used to solve the static problems for ellipsoids and its limiting forms (disks, needles), for a half-plane, wedge, plane with an elliptical aperture, hyperboloid of revolution, parabaloid of revolution, cone, thin spherical shell, spherical segment, two conducting spheres, and some other problems. Electrostatic fields in a flaky (layered) medium with parallel and sectorial boundaries have been studied [33], [143]. Some of the problems were solved in closed form using integral equations, e.g., the problems for a disk, spherical shell, plane with a circular hole, etc. Wiener-Hopf, dual, and singular integral equations were used [33], [143], [76], [164]. Electrostatic problems for a finite circular hollow cylinder (tube) were studied in [158] by numerical methods. The capacitance per unit length of the tube and the polarizability of the tube were calculated. The authors reduced the integral equation for the surface charge to an infinite system of linear algebraic equations and solved the truncated system on a computer. Their method depends heavily on the particular geometry of the problem and does not allow one to handle any local perturbations of the shape of the tube. In [68] the variational methods of Ritz, Trefftz, the Galerkin method, and the grid method are discussed in connection with the static problems. However, no specific properties of these problems are used. These methods are presented in a more general setting in [53], [66]. In practice, these methods are time-consuming, and variational methods in three-dimensional static problems probably have some advantages over the grid method. A vast literature exists on the calculation of the capacitances of perfect conductors [43], [79]. In [43] there is a reference section which gives the capacitances of conductors of certain shapes. In [78], [79] a systematic exposition of variational methods for estimation of the capacitances and other functionals of practical interest is given. In [153] there are some programs for calculating the two-dimensional static fields using integral equations method. In [148] some geometrical properties of the lines of electrical field strength are used for approximate calculations of the field. This approach is empirical. One of the objectives of this book is to present systematically the usage of integral equations for calculating static fields and some practically useful functionals of these fields, in particular, capacitances and polarizability tensors of bodies of arbitrary shape. The method gives approximate analytical formulas for calculations of these functionals with the desired accuracy. These formulas can be used to construct a computer program for calculating capacitances and polarizability tensors. The many-body problems are also discussed as well as the problems for flaky-homogeneous bodies, e.g., coated particles. Two-sided variational estimates of capacitances and polarizability tensors are given. The problems for open thin metallic screens are considered as well as those for perfect magnetic films. Calculating the magnetic polarizability of perfect magnetic films is important because such films are used as memory elements of computers. The above-mentioned formulas for capacitances and polarizhbility tensors allow one to give approximate analytical formulas for the scattering matrix in the problem of wave scattering by small bodies of arbitrary shape. This is done for scalar and electromagnetic waves. The dependence of the scattering matrix on the boundary conditions on the surface of the scatterer is investigated. The wave scattering in a medium consisting of many small particles is studied and equations for the effective (self-consistent) field in such a medium are derived. This makes it possible to discuss the inverse problem of determining the properties of such a medium from knowledge of the waves scattered by this medium.