Stable homotopy groups are a concept in algebraic topology that study the behavior of topological spaces when they are "stabilized" by taking products with spheres. Specifically, the stable homotopy groups of a space are defined as the direct limit of its homotopy groups as the dimension of the spheres increases. This allows mathematicians to analyze properties of spaces that remain unchanged under certain transformations. These groups are denoted as π_n^s and are particularly important in the study of stable homotopy theory, which focuses on the relationships between different topological spaces. They provide insights into the structure of topological manifolds and have applications in various fields, including algebraic topology and homological algebra.