"The Theory of Riemannian Algebraic Functions" is an outstanding work of the mathematician Felix Klein, devoted to the study of Riemannian algebraic functions. In his book, the author considers the main ideas, theorems and methods related to algebraic functions, which open new horizons for the development of mathematics. Thanks to his work, readers get the opportunity to gain a deeper understanding of complex mathematical concepts and their application in the grand theory of functions. The book "Riemann Theory of Algebraic Functions" has become a classic source of knowledge for mathematicians all over the world, opening the door to the unique world of analysis and algebra.