Some mathematical questions of theory of information transmission

A survey, talk given by M.S. Pinsker at the Summer Seminar on Information Theory and Statistical Methods of Automatic Control, Prague, May 25 - June 4, 1965, was published in Kybernetika Journal of the Czech Academy of Sciences (1966, vol. 2, no. 2, pp. 117-146). BY the courtesy of the editors of Kybernetika, we are allowed to publish an abridged version of the talk, which concisely and clearly exposes final mathematical results that underlie Shannon's information theory. The content of the talk is deeply intertwined with the author's works. The talk is almost unknown to Russian readers, and with this publication we fill this gap, thereby paying tribute to our outstanding scientist and friend.