This book studies classes of linear integral equations of the first kind most often met in applications. Since the general theory of integral equations of the first kind has not been formed yet, the book considers the equations whose solutions either are estimated in quadratures or can be reduced to well-investigated classes of integral equations of the second kind.In this book the theory of integral equations of the first kind is constructed by using the methods of the theory of functions both of real and complex variables. Special attention is paid to the inversion formulas of model equations most often met in physics, mechanics, astrophysics, chemical physics etc. The general theory of linear equations including the Fredholm, the Noether, the Hausdorff theorems, the Hilbert-Schmidt theorem, the Picard theorem and the application of this theory to the solution of boundary problems are given in this book. The book studies the equations of the first kind with the Schwarz Kernel, the Poisson and the Neumann kernels; the Volterra integral equations of the first kind, the Abel equations and some generalizations, one-dimensional and many-dimensional analogues of the Cauchy type integral and some of their applications.
Theory of the linear equations in metric spaces; general remarks with respect to linear integral equations of the first kind; the Piard's theorem of solvability of one class of integral equations of the first kind; integral equations with kernels, generated by Schwarz kernel; integral equations of the first kind with kernels generated by Poison's and Schwarz's kernels; some other classess of integral equations of the first kind; Abel's integral equation and some of its generalizations; two-dimensional analog of the Cauchy type integral and some of its applications.