Andrew Casson has conducted pioneering work in low-dimensional topology. His two best-known contributions are his invention of Casson handles for 4-manifolds (later used by Michael Freedman to classify simply connected four-dimensional manifolds), and his introduction of the Casson invariant, which was the first of a family of new invariants of 3-manifolds related to quantum field theory. Other important contributions include his joint discovery of the Casson–Gordon invariant in knot theory, his unpublished thesis on surgery and triangulations of topological manifolds, and his recent proof of an old conjecture about Seifert fibered manifolds.