Homotopy groups are algebraic structures in the field of topology that help classify spaces based on their shape and connectivity. They are defined using continuous maps from spheres into a given topological space, capturing information about the space's loops and higher-dimensional analogs. The most basic homotopy group is the fundamental group, which considers loops based at a point. Higher homotopy groups, denoted as π_n, extend this concept to spheres of dimension n. For example, π_2 involves maps from a 2-dimensional sphere. These groups provide insights into the properties of spaces, such as whether they can be continuously deformed into one another, which is essential in algebraic topology.