  The COntractor REnormalization group (CORE) approximation, a new method for
solving Hamiltonian lattice systems, is introduced. The approach combines
variational and contraction techniques with the real-space renormalization
group approach and is systematically improvable. Since it applies to lattice
systems of infinite extent, the method is suitable for studying critical
phenomena and phase structure; systems with dynamical fermions can also be
treated. The method is tested using the 1+1-dimensional Ising model.
