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This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the flrst kind and related background material on inverse problems. We begin with an historical introduction to the fleld of integral equations of the flrst kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the flrst kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided.

Integral equations of the first kind, inverse problems and regularization: a crash course