The Casson invariant is a mathematical concept used in the field of topology, specifically in the study of 3-manifolds. It provides a way to classify certain types of manifolds by assigning them a numerical value, which helps in understanding their structure and properties. The invariant is particularly significant for homology 3-spheres, which are 3-dimensional spaces that resemble a sphere in terms of their homology. Developed by Andrew Casson in the 1980s, the Casson invariant is linked to the study of surgery theory and knot theory. It plays a crucial role in distinguishing between different manifolds and has applications in various areas of mathematics, including gauge theory and quantum topology.