The author's monograph "The Theory of Rings" is well known to the Soviet reader Its Russian translation was published in 1947. In his new monograph "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 there was a rapid development of this theory, which completely changed 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 algebra.