"The Theory of Partial Algebraic Operations" offers a comprehensive examination of algebraic operations and their relationships. In modern algebra, the theory of algebraic operations is considered central, with a focus on the study of both complete and partial operations. This work highlights the intrinsic nature of the fundamental concepts and problems of algebra, as well as the consistency of their methods. The significance of partial operations, which are important in various fields of mathematics such as category theory, formal language theory, and information theory, is particularly emphasized. Authors E. S. Ljapin and A. E. Evseev provide a thorough analysis in this textbook that covers both theoretical and practical aspects of algebra, thus making a valuable contribution to the mathematical literature.