Symmetries of Compact Riemann Surfaces This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries namely the number of conjugacy classes of symmetries the numbers of ovals of symmetries and the symmetry types of Riemann surfaces Preliminaries On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces Counting Ovals of Symmetries of Riemann Surfaces Symmetry Types of Some Families of Riemann Surfaces Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms