  Connes and Kreimer have discovered a Hopf algebra structure behind
renormalization of Feynman integrals. We generalize the Hopf algebra to the
case of ribbon graphs, i.e. to the case of theories with matrix fields. The
Hopf algebra is naturally defined in terms of surfaces corresponding to ribbon
graphs. As an example, we discuss renormalization of $\Phi^4$ theory and the
1/N expansion.
