"Symmetries of Compact Riemann Surfaces" is a comprehensive monograph that deals with the symmetries of compact Riemann surfaces. These symmetries, defined as anti-analytic involutions, play a crucial role in the theory of Riemann surfaces. The authors explore the relationship between Riemann surfaces with symmetries and algebraic curves that can be defined over the real numbers. The work addresses three central themes related to the topology of symmetries: the number of conjugacy classes of symmetries, the number of ovals of symmetries, and the symmetry types of Riemann surfaces. This monograph is aimed at professionals and students of mathematics who seek a deeper understanding of the geometric and topological properties of Riemann surfaces. It offers valuable insights into the complex structures and their symmetries that are significant for modern mathematics.