Editorial: S. N. Mergelyan's Dissertation "Best Approximations in the Complex Domain".

This document is an editorial that presents an authentic translation of Sergey N. Mergelyan's dissertation titled "Best Approximations in the Complex Domain." Mergelyan was a renowned Soviet and Armenian mathematician known for his work in approximation theory and the theory of functions of complex variables. The dissertation discusses Mergelyan's research on various topics, including polynomial approximation, uniform approximation by harmonic functions, and the approximation of continuous functions. Mergelyan's theorem on approximation by polynomials is highlighted as a significant contribution to the field. The document also acknowledges the individuals involved in the publication of Mergelyan's dissertation. [Extracted from the article]