History of Science and Engineering Annotation << Back L. Euler’s Creation of FouNdations the Combinatorial Theory of Latin Squares А.Е. Маlykh V.I. Danilova It was ascertained that an occasion to Euler’s creation of theoretical foundation of Latin squares served a problem of 36 officers and its generalization. Unsuccessful attempts of its decision for two centuries were examined. In article found out that Euler introduced new notions and terms, proved theorems, created methods construction of Latin squares and their orthogonal pairs; studied the structure, elaborated modes of its identification, solved some questions in the theory of enumeration. Key words: Latin square; orthogonal pair; transversal; combinatorial invariants; methods of description; modes of construction; finite geometries; error detecting and correcting codes; experimental designs. E-mail: malych@pspu.ru, E-mail: vi-dan@mail.ru. Pp. 2-7