Symmetric spaces are a type of geometric structure where the properties remain unchanged under certain transformations. Specifically, they exhibit symmetry around points, meaning that for any point in the space, there is a way to reflect or rotate around that point, resulting in a configuration that looks the same. This concept is important in various fields, including mathematics, physics, and computer science. These spaces can be classified into two main types: Riemannian symmetric spaces and pseudo-Riemannian symmetric spaces. Riemannian symmetric spaces have a positive-definite metric, while pseudo-Riemannian spaces can have indefinite metrics. Both types are studied for their rich geometric properties and applications in areas like differential geometry and theoretical physics.