A homotopy group is a concept in algebraic topology that captures information about the shape or structure of a topological space. It is defined using continuous maps from spheres into the space, allowing mathematicians to study how these maps can be deformed into one another. The most basic homotopy group is the first homotopy group, also known as the fundamental group, which describes loops in the space. Homotopy groups are denoted as π_n(X), where X is the topological space and n indicates the dimension of the sphere being mapped. These groups help classify spaces up to homotopy equivalence, providing insights into their topological properties. They are essential in understanding concepts like homotopy equivalence, topological spaces, and algebraic topology.