Madsen's Theorem for Homotopy Groups is a significant result in algebraic topology, particularly concerning the stable homotopy groups of spheres. It states that the stable homotopy groups of spheres can be computed using the homology of certain infinite loop spaces, specifically the Madsen-Tillmann spectrum. This theorem connects the topology of manifolds with algebraic structures, providing insights into the behavior of these groups. The theorem has implications for the study of manifold theory and homotopy theory, as it helps to understand how different topological spaces relate to one another. Madsen's Theorem also plays a role in the broader context of stable homotopy theory, where researchers explore the properties of spaces that remain invariant under suspension.