H-spaces from a homotopy point of view.- The Hopf construction.- The projective plane.- Maps into an H-space: Algebraic structure, inverses, other multiplications, etc.- Associativity: Loop spaces and topological groups.- H-spaces which are finite complexes.- The bar construction spectral sequence.- Homotopy associativity.- Maps of H-spaces.- Spaces induced by H-maps.- Differentials in the bar construction.- An-spaces.- Massey products and generalized bar construction.- Homotopy commutativity.- Structure on BX.- Infinite loop spaces.- Operations in iterated loop spaces.