From the publisher: The author's previous monograph is well known to the reader. Its Russian translation was published in 1947. In his new monograph "The Construction of Rings", the author for the first time systematizes the rich material accumulated in the theory of associative rings and algebras over the past 10-12 years, during which the rapid development of this theory took place, completely changing its face. Reading the book gives a clear idea of the current state of the mentioned theory and the main trends in its development. The monograph is intended for algebraic mathematicians; it will also be useful for students and graduate students of universities and pedagogical institutes specializing in the field of algebra.