Jim Stasheff is an American mathematician with fundamental contributions to algebraic topology and homological algebra. He is famous for having discovered the Stasheff polytopes which govern the algebraic structure of loop spaces. The combinatorics of the polytopes had an enormous influence on the theory of operads and on the emergence of higher category theory. His theory of homotopy -spaces is the starting point of the theory of homotopy invariant algebraic structures.
The book of Milnor and Stasheff Characteristic classes is a classic in topology.