Symmetry in Modern Geometry

This lecture covers the fundamental concepts of symmetry in modern geometry, including isometries, reflections, rotations, and translations. It explores the properties left invariant by different types of geometrical transformations, such as isometries and homotheties. The lecture also delves into the distinction between rotations of arbitrary angles and rotations of 180 degrees, emphasizing the importance of the latter in preserving certain properties. Additionally, it discusses the concept of involution and the composition of multiple reflections to generate various isometries. The lecture concludes by highlighting the significance of axial reflections and their role in constructing different types of isometries.