The monograph is devoted to topical issues related to the choice of multidimensional signal ensembles for the designed communication systems, which allow transmitting messages over communication channels with the highest possible speed (maximum spectral efficiency), as well as with maximum energy efficiency, the theoretical limit of which was established by the creator of information theory Claude Shannon. It provides an analytical review of the main modern methods for constructing noise-resistant codes designed for transmitting messages in discrete communication channels, and two-dimensional and multidimensional signal ensembles, with the help of which messages are transmitted in continuous communication channels. The monograph presents a number of new results.