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.