The classical approach organizes this structure via operads, while the recent approach of Jacob Lurie deals with it using -operads in -categories.
Stasheff's research contributions include the study of associativity in loop spaces and the construction of the associahedron (also called the Stasheff polytope), ideas leading to the theory of operads; homotopy theoretic approaches to Hilbert's fifth problem on the characterization of Lie groups; and the study of Poisson algebras in mathematical physics.