Geometric inversion is a transformation in geometry that maps points in a plane or space to new locations based on their distance from a fixed point, called the center of inversion. This process involves drawing a circle with a specific radius around the center, where points inside the circle are moved outside and vice versa, maintaining a specific relationship between distances. Inversion has interesting properties, such as transforming circles into other circles or lines, depending on their position relative to the center. It is often used in advanced mathematics and has applications in fields like complex analysis and topology.