[Author] Bliudze, Simon. [Title] Optimal multidimensional continued fractions [AMS Subj-class] 11Jxx Diophantine approximation, transcendental number theory [See also 11K60] 11J70 Continued fractions and generalizations [See also 11A55, 11K50] [Keywords] Diophantine approximation, Continued fractions, Jacobi-Perron algorithm [Abstract] The paper in Russian is the dissertation submitted by the author in 1998 to fulfil the requirements of the Department of Mathematics and Mechanics of the Saint-Petersburg State University (Russia) for obtaining the Specialist degree. The dissertation was prepared under the supervision of Prof. Andrei A. Lodkin. The main objective of the presented work was a search of candidates for the multidimensional generalisation of the golden ratio, based on its interpretation as a continued fraction. [Comments] R ussian, 18 pp., with an English foreword by the author and a Russian one by A. Lodkin [Contact e-mail] simon.bliudze@inria.fr