The book of G. Segueux, the translation of which is offered to the attention of Soviet readers, is devoted not only to the research carried out by its author - the whole general theory of orthogonal polynomials with all its main applications is presented in a systematic and clear form. The book of G. Segyo, the first edition of which was published in 1939, was preceded only by a monograph by J. Shokhat (1934) on the general theory of orthogonal polynomials, but most of the results are given without evidence.