Homotopy of pseudosimplicial groups, nonabelian derived functors, and algebraic $K$-theory

Using the homotopy groups of pseudosimplicial groups, we construct nonabelian derived functors with values in the category of groups. This enables us to obtain algebraic $K$-theory in the category of associative rings as the theory of left derived functors of the covariant functor $GL$.
Bibliography: 20 titles.