Donaldson invariants are mathematical tools used in the field of differential geometry, particularly in the study of smooth four-manifolds. They are derived from gauge theory and provide a way to classify these manifolds based on their topological properties. These invariants help distinguish between different types of four-manifolds that may appear similar at first glance. The concept was introduced by Simon Donaldson in the 1980s, revolutionizing the understanding of four-dimensional topology. Donaldson invariants are computed using solutions to the Yang-Mills equations and can reveal information about the manifold's structure, such as its curvature and the presence of certain types of surfaces.