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Cambridge University Press, 1958. - 172 pages.The present work is intended as a successor to Maxime Bocher's tract An introduction to the study of integral equations, which has long been out of print. It is devoted entirely to non-singular linear integral equations, that is, those for which the main results of the Fredholm theory are valid. Only a brief indication of the important applications to differential equations is given, in § 1-2 of the Introduction.The theory is not presented in terms of linear operators in Hilbert space or a more general topological vector space; this has enabled me to obtain stronger results on the convergence of the various expansions than would have been possible in a more general context. On the other hand, I have made extensive use of the notations of operator theory; many of the formulae thus become much briefer and easier to read.
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